a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

kernel weighted gmm estimators for linear time series models abstract this paper analyzes the higher order asymptotic properties of generalized method of moments gmm estimators for linear time series models using many lags as instruments a data dependent moment selection method based on minimizing the approximate mean squared error is developed in addition a new version of the gmm estimator based on kernel weighted moment conditions is proposed it is shown that kernel weighted gmm estimators can reduce the asymptotic bias compared to standard gmm estimators kernel weighting also helps to simplify the problem of selecting the optimal number of instruments a feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted gmm estimator

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

partially linear hazard regression with varying coefficients for multivariate survival data summary the paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data a profile pseudo partial likelihood estimation method is proposed the estimation of the parameters of the linear part is accomplished via maximization of the profile pseudo partial likelihood whereas the varying coefficient functions are considered as nuisance parameters that are profiled out of the likelihood it is shown that the estimators of the parameters are root n consistent and the estimators of the non parametric coefficient func tions achieve optimal convergence rates asymptotic normality is obtained for the estimators of the finite parameters and varying coefficient functions consistent estimators of the asymptotic variances are derived and empirically tested which facilitate inference for the model we prove that the varying coefficient functions can be estimated as well as if the parametric components were known and the failure times within each subject were independent simulations are con ducted to demonstrate the performance of the estimators proposed a real data set is analysed to illustrate the methodology proposed

unified lasso estimation by least squares approximation we propose a method of least squares approximation lsa for unified yet simple lasso estimation our general theoretical framework includes ordinary least squares generalized linear models quantile regression and many others as special cases specifically lsa can transfer many different types of lasso objective functions into their asymptotically equivalent least squares problems thereafter the standard asymptotic theory can be established and the lars algorithm can be applied in particular if the adaptive lasso penalty and a bayes information criterion type tuning parameter selector are used the resulting lsa estimator can be as efficient as the oracle extensive numerical studies confirm our theory

bootstrap inference for instrumental variable models with many weak instruments this study s main contribution is to theoretically analyze the application of bootstrap methods to instrumental variable models when the available instruments may be weak and the number of instruments goes to infinity with the sample size we demonstrate that a standard residual based bootstrap procedure cannot consistently estimate the distribution of the limited information maximum likelihood estimator or fuller 1977 estimator under many many weak instrument sequence the primary reason is that the standard procedure fails to capture the instrument strength in the sample adequately in addition we consider the restricted efficient re bootstrap of davidson and mackinnon 2008 2010 2014 that generates bootstrap data under the null restricted and uses an efficient estimator of the coefficient of the reduced form equation efficient we find that the re bootstrap is also invalid however it effectively mimics more key features in the limiting distributions of interest and thus is less distorted in finite samples than the standard bootstrap procedure finally we propose modified bootstrap procedures that provide a valid distributional approximation for the two estimators with many many weak instruments a monte carlo experiment shows that hypothesis testing based on the asymptotic normal approximation can have severe size distortions in finite samples instead our modified bootstrap procedures greatly reduce these distortions

wavelet thresholding for non necessarily gaussian noise idealism for various types of noise exponential normal mixture compactly supported wavelet thresholding methods are studied problems linked to the existence of optimal thresholds are tackled and minimaxity properties of the methods also analyzed a coefficient dependent method for choosing thresholds is also briefly presented

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

on the implementation of singly implicit runge kutta methods a modified newton method is often used to solve the algebraic equations that arise in the application of implicit runge kutta methods when the runge kutta method has a coefficient matrix a with a single point spectrum with eigenvalue a the efficiency of the modified newton method is much improved by using a similarity transformation of a each iteration involves vector transformations in this article an alternative iteration scheme is obtained which does not require vector transformations and which is simpler in other respects also both schemes converge in a finite number of iterations when applied to linear systems of differential equations but the new scheme uses the nilpotency of a ai to achieve this numerical results confirm the predicted convergence for nonlinear systems and indicate that the scheme may be a useful alternative to the modified newton method for low dimensional systems the scheme seems to become less effective as the dimension increases however it has clear advantages for parallel computation making it competitive for high dimensional systems

least squares model averaging this paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models existing model average methods are based on exponential akaike information criterion aic and bayesian information criterion bic weights in distinction this paper proposes selecting the weights by minimizing a mallows criterion the latter an estimate of the average squared error from the model average fit we show that our new mallows model average mma estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators in a simulation experiment we show that the mma estimator compares favorably with those based on aic and bic weights the proof of the main result is an application of the work of li 1987

analysis of energy and quadratic invariant preserving equip methods abstract in this paper we are concerned with the analysis of a class of geometric integrators at first devised in brugnano et al 2010 and brugnano et al 2012 which can be regarded as an energy conserving variant of gauss collocation methods with these latter they share the property of conserving quadratic first integrals but in addition they also conserve the hamiltonian function itself we here reformulate the methods in a more convenient way and propose a more refined analysis than that given in brugnano et al 2012 also providing as a by product a practical procedure for their implementation a thorough comparison with the original gauss methods is carried out by means of a few numerical tests solving hamiltonian and poisson problems

review paper efficient numerical methods for the solution of stiff initial value problems and differential algebraic equations in recent years after a prolonged period of intense activity the study of numerical methods for solving stiff initial value problems for ordinary differential equations and differential algebraic equations has reached a certain maturity there now exist some excellent codes which are both efficient and reliable for solving these particular classes of problems in this paper we sketch some of the main theory which underpins stiff integration methods and we use this to describe and put into context some of the best codes currently available by referencing only codes which have been thoroughly tested and are widely available our aim is to direct users of numerical software to those codes which they should try initially if faced with the problem of solving ordinary differential equations of this type an additional feature is that the codes which we propose serve as benchmarks against which any new codes can be evaluated

algebraically stable and implementable runge kutta methods of high order there are three interesting properties of methods for stiff ordinary differential equations order stability and efficiency of implementation this paper constructs runge kutta methods of orders 5 and 6 which possess these properties to a high extent we further classify all algebraically stable methods of an arbitrary order and give various relationships between contractivity and order of implicit methods

galerkin runge kutta discretizations for parabolic equations with time dependent coefficients a new class of fully discrete galerkin runge kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients unlike any classical counterpart this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction in support of this claim error estimates are proved and computational results are presented additionally since the time stepping equations involve coefficient matrices changing at each time step a preconditioned iterative technique is used to solve the linear systems only approximately nevertheless the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients furthermore it is noted that special runge kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method

stratified partial likelihood estimation when multiple durations are generated by a single unit they may be related in a way that is not fully captured by the regressors the omitted unit specific variables might vary over the durations they might also be correlated with the variables in the regression component we propose an estimator that responds to these concerns and develop a specification test for detecting unobserved unit specific effects data from malaysia reveal that concentration of child mortality in some families is imperfectly explained by observed explanatory variables and that failure to control for unobserved heterogeneity seriously biases the parameter estimates

cue with many weak instruments and nearly singular design abstract this paper analyzes many weak moment asymptotics under the possibility of similar moments the possibility of highly related moments arises when there are many of them knight and fu 2000 designate the issue of similar regressors as the nearly singular design in the least squares case in the nearly singular design the sample variance converges to a singular limit term however knight and fu 2000 assume that on the nullspace of the limit term the difference between the sample variance and the singular matrix converges in probability to a positive definite matrix when multiplied by an appropriate rate we consider specifically continuous updating estimator cue with many weak moments under nearly singular design we show that the nearly singular design affects the form of the limit of the many weak moment asymptotics that is introduced by newey and windmeijer 2009a however the estimator is still consistent and the wald test has the standard 2 limit

choosing instrumental variables in conditional moment restriction models properties of gmm estimators are sensitive to the choice of instrument using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and or variance in small samples in this paper we develop and implement asymptotic mean square error mse based criteria for instrument selection in estimation of conditional moment restriction models the models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity we develop moment selection criteria for the familiar two step optimal gmm estimator gmm a bias corrected version and generalized empirical likelihood estimators gel that include the continuous updating estimator cue as a special case we also find that the cue has lower higher order variance than the bias corrected gmm estimator and that the higher order efficiency of other gel estimators depends on conditional kurtosis of the moments

flood frequency analysis using the cox regression model procedures for incorporating time varying exogenous information into flood frequency analyses are developed using the cox regression model for counting processes in this statistical model the probability of occurrence of a flood peak in a short interval t t dt depends in an explicit manner on the values at t of k covariate processes z1 zk specifically letting dn t be 1 if a flood peak occurs in t t dt and 0 otherwise dn t a t exp j 1kbjzj t dm t where a the baseline intensity is an unknown function b is a vector of unknown regression parameters and the error dm t is conditionally orthogonal to the past history two applications assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time varying flood frequency estimates are considered

panel data models with multiple time varying individual effects abstract this paper considers a panel data model with time varying individual effects the data are assumed to contain a large number of cross sectional units repeatedly observed over a fixed number of time periods the model has a feature of the fixed effects model in that the effects are assumed to be correlated with the regressors the unobservable individual effects are assumed to have a factor structure for consistent estimation of the model it is important to estimate the true number of individual effects we propose a generalized methods of moments procedure by which both the number of individual effects and the regression coefficients can be consistently estimated some important identification issues are also discussed our simulation results indicate that the proposed methods produce reliable estimates

shrinkage tuning parameter selection with a diverging number of parameters contemporary statistical research frequently deals with problems involving a diverging number of parameters for those problems various shrinkage methods e g the lasso and smoothly clipped absolute deviation are found to be particularly useful for variable selection nevertheless the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters with a fixed predictor dimension wang and co worker have demonstrated that the tuning parameters selected by a bayesian information criterion type criterion can identify the true model consistently in this work similar results are further extended to the situation with a diverging number of parameters for both unpenalized and penalized estimators consequently our theoretical results further enlarge not only the scope of applicability of the traditional bayesian information criterion type criteria but also that of those shrinkage estimation methods

the l 1 method for robust nonparametric regression abstract consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy tailed error distribution the two standard approaches to such a problem are each flawed robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods which are not resistant against outliers existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares neither of these two approaches combines computational ease with asymptotic theoretical results furthermore application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable in this article a new hybrid method is propose

properties of the cue estimator and a modification with moments abstract in this paper we analyze properties of the continuous updating estimator cue proposed by hansen et al 1996 which has been suggested as a solution to the finite sample bias problems of the two step gmm estimator we show that the estimator should be expected to perform poorly in finite samples under weak identification in particular the estimator is not guaranteed to have finite moments of any order we propose the regularized cue rcue as a solution to this problem the rcue solves a modification of the first order conditions for the cue estimator and is shown to be asymptotically equivalent to cue under many weak moment asymptotics our theoretical findings are confirmed by extensive monte carlo studies

generalized method of moments with many weak moment conditions using many moment conditions can improve efficiency but makes the usual generalized method of moments gmm inferences inaccurate two step gmm is biased generalized empirical likelihood gel has smaller bias but the usual standard errors are too small in instrumental variable settings in this paper we give a new variance estimator for gel that addresses this problem it is consistent under the usual asymptotics and under many weak moment asymptotics is larger than usual and is consistent we also show that the kleibergen 2005 lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments in addition we introduce a jackknife gmm estimator but find that gel is asymptotically more efficient under many weak moments in monte carlo examples we find that t statistics based on the new variance estimator have nearly correct size in a wide range of cases

stability of collocation at gaussian points symmetric runge kutta schemes are particularly useful for solving stiff two point boundary value problems such a stable schemes perform well in many cases but it is demonstrated that in some instances the stronger property of algebraic stability is required a characterization of symmetric algebraically stable runge kutta schemes is given the class of schemes thus defined turns out not to be very rich the only collocation schemes in it are those based on gauss points and other schemes in the class do not seem to offer any advantage over collocation at gaussian points

dynamical properties of hybrid systems simulators this paper analyzes the dynamical properties of a class of hybrid systems simulators a hybrid system is a dynamical system with a state that can both flow and jump its simulator attempts to generate its solutions approximately the paper presents mild regularity conditions on the hybrid system and its simulator to guarantee that simulated solutions are close to actual solutions on compact hybrid time intervals and that asymptotically stable compact sets are preserved in a semiglobal practical sense under simulation in fact it is established that asymptotically stable compact sets are continuous in the integration step size parameter of the simulator that is as the step size of the simulator converges to zero the asymptotically stable set observed in simulations approaches the asymptotically stable compact set of the true hybrid system examples are used to illustrate concepts and results

regularized liml for many instruments the use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators however in finite samples the inclusion of an excessive number of moments increases the bias to solve this problem we propose regularized versions of the limited information maximum likelihood liml based on three different regularizations tikhonov landweber fridman and principal components our estimators are consistent and asymptotically normal under heteroskedastic error moreover they reach the semiparametric efficiency bound assuming homoskedastic error we show that the regularized liml estimators possess finite moments when the sample size is large enough the higher order expansion of the mean square error mse shows the dominance of regularized liml over regularized two staged least squares estimators we devise a data driven selection of the regularization parameter based on the approximate mse a monte carlo study and two empirical applications illustrate the relevance of our estimators

near exogeneity and weak identification in generalized empirical likelihood estimators many moment asymptotics abstract this paper investigates the generalized empirical likelihood gel estimators when there are local violations of the exogeneity condition near exogeneity in the case of many weak moments we also examine the tradeoff between the degree of violation of the exogeneity and the number of nearly exogenous instruments in this respect this paper extends many weak moment asymptotics of newey and windmeijer 2009a the overidentifying restrictions test can detect both mild and large violations of exogeneity in the case of minor violations the anderson rubin 1949 and wald tests are not size distorted

model averaging by jackknife criterion in models with dependent data abstract the past decade witnessed a literature on model averaging by frequentist methods for the most part the asymptotic optimality of various existing frequentist model averaging estimators has been established under i i d errors recently hansen and racine hansen b e racine j 2012 jackknife model averaging journal of econometrics 167 38 46 developed a jackknife model averaging jma estimator which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors in this paper we broaden hansen and racine s scope of analysis to encompass models with i a non diagonal error covariance structure and ii lagged dependent variables thus allowing for dependent data we show that under these set ups the jma estimator is asymptotically optimal by a criterion equivalent to that used by hansen and racine a monte carlo study demonstrates the finite sample performance of the jma estimator in a variety of model settings

simultaneous selection and weighting of moments in gmm using a trapezoidal kernel abstract this paper proposes a novel procedure to estimate linear models when the number of instruments is large at the heart of such models is the need to balance the trade off between attaining asymptotic efficiency which requires more instruments and minimizing bias which is adversely affected by the addition of instruments two questions are of central concern 1 what is the optimal number of instruments to use 2 should the instruments receive different weights this paper contains the following contributions toward resolving these issues first i propose a kernel weighted generalized method of moments gmm estimator that uses a trapezoidal kernel this kernel turns out to be attractive to select and weight the number of moments second i derive the higher order mean squared error of the kernel weighted gmm estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels finally monte carlo simulations show that in finite samples the kernel weighted gmm estimator performs on par with other estimators that choose optimal instruments and improves upon a gmm estimator that uses all instruments

efficiently implementable algebraically stable runge kutta methods recent work by butcher bit 16 1976 pp 237 240 on the implementation of implicit runge kutta methods has shown that if his technique is used the most efficiently implementable methods are those whose runge kutta matrix has a single real eigenvalue in this paper therefore we analyze the algebraic stability of two families of methods with this property namely singly implicit and diagonally implicit methods

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

time consistent fluid structure interaction on collocated grids for incompressible flow abstract consistent time integration on collocated grids for incompressible flow has been studied for static grids using the piso method in which the dependencies on time step size and under relaxation has been studied in detail however for moving grids a detailed description is still missing therefore a step by step analysis of a time consistent fluid structure interaction fsi method for incompressible flow on collocated grids is presented the method consist of face normal and area correction for moving grids treatment of velocity boundary conditions for no slip walls time integration of structure equations and fluid force interpolation to structure the basis of the method is the piso method of the incompressible navier stokes equations time consistency on static grids is shown first after which time consistency on moving grids is described and analyzed for moving grids consistent time integration is described in two ways 1 constructing the face velocities from a normal and tangential component and 2 correcting the face flux with a face normal and face area correction for both descriptions the general formulation for the backward differencing schemes bdf are given and the correct behavior of the first second and third order schemes is demonstrated by means of an academic test case circular cavity flow additionally the force coupling from the fluid to the structure is discussed in detail for combining a fourth order explicit runge kutta scheme for the structure with a bdf scheme for the fluid three interpolations for the fluid forces are shown which result in either a first order or second order fsi scheme third order fsi is demonstrated when the third order bdf scheme is applied on both the structure and fluid equations also under relaxation for the fluid equations is considered and it is demonstrated that the order of the three bdf schemes are independent of the under relaxation factor finally the proposed method of time consistent fsi on collocated grids for incompressible flows is demonstrated by applying it to a three dimensional flow over an elastic structure in a channel and the cylinder flap fsi benchmark case of turek and hron

high order algebraically stable multistep runge kutta methods in this paper we examine some of the stability properties of a special class of multivalue methods called in k burrage order properties of multivalue methods ima j numer anal submitted multistep runge kutta methods and construct families of algebraically stable methods of arbitrarily high order

testing identification strength we consider models defined by a set of moment restrictions that may be subject to weak identification following the recent literature the identification of the structural parameters is characterized by the jacobian of the moment conditions we unify several definitions of identification that have been used in the literature and show how they are linked to the consistency and asymptotic normality of gmm estimators we then develop two tests to assess the identification strength of the structural parameters in models that are i either linear or separable ii neither linear nor separable both tests are straightforward to apply and allow to test specific subvectors without assuming identification of the components not under test in simulations our tests are well behaved when compared to contenders both in terms of size and power in addition we show how pretesting specific subvectors can improve inference by delivering shorter confidence regions with comparable coverage probability finally when applied to the estimation of the elasticity of intertemporal substitution our test indicates weak instruments in a larger number of countries than tests proposed by stock and yogo 2005 and montiel olea and pflueger 2012

instrumental variable estimation in the presence of many moment conditions abstract this paper develops shrinkage methods for addressing the many instruments problem in the context of instrumental variable estimation it has been observed that instrumental variable estimators may behave poorly if the number of instruments is large this problem can be addressed by shrinking the influence of a subset of instrumental variables the procedure can be understood as a two step process of shrinking some of the ols coefficient estimates from the regression of the endogenous variables on the instruments then using the predicted values of the endogenous variables based on the shrunk coefficient estimates as the instruments the shrinkage parameter is chosen to minimize the asymptotic mean square error the optimal shrinkage parameter has a closed form which makes it easy to implement a monte carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures

an efficient family of strongly a stable runge kutta collocation methods for stiff systems and daes part i stability and order results for each integer s 3 a new uniparametric family of stiffly accurate strongly a stable s stage runge kutta methods is obtained these are collocation methods with a first internal stage of explicit type the methods are based on interpolatory quadrature rules with precision degree equal to 2s 4 and all of them have two prefixed nodes c 1 0 and c s 1 the amount of implicitness of our s stage method is similar to that involved with the s stage lobattoiiia method or with the s 1 stage radauiia method the new family of runge kutta methods proves to be of interest for the numerical integration of stiff systems and differential algebraic equations in fact on several stiff test problems taken from the current literature two methods selected in our 4 stage family seem to be slightly more efficient than the 3 stage radauiia method and also more robust than the 4 stage lobattoiiia method

conditional moment models under semi strong identification we consider conditional moment models under semi strong identification identification strength is directly defined through the conditional moments that flatten as the sample size increases our new minimum distance estimator is consistent asymptotically normal robust to semi strong identification and does not rely on the choice of a user chosen parameter such as the number of instruments or some smoothing parameter heteroskedasticity robust inference is possible through wald testing without prior knowledge of the identification pattern simulations show that our estimator is competitive with alternative estimators based on many instruments being well centered with better coverage rates for confidence intervals

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

jackknife instrumental variable estimation with heteroskedasticity we present a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity it weighs observations such that many instruments consistency is guaranteed while the signal component in the data is maintained we show that this results in a smaller signal component in the many instruments asymptotic variance when compared to estimators that neglect a part of the signal to achieve consistency both many strong instruments and many weak instruments asymptotic distributions are derived using high level assumptions that allow for instruments with identifying power that varies between explanatory variables standard errors are formulated compactly we review briefly known estimators and show in particular that our symmetric jackknife estimator performs well when compared to the hlim and hful estimators of hausman et al in monte carlo experiments

score tests for homogeneity of regression effect in the proportional hazards model a simple model containing the proportional hazards regression model as a special case is presented the purpose of the model is to provide a framework in which specific alternatives to the proportional hazards assumption may be tested rank invariant score tests for linear quadratic or exponential trends can for instance all be undertaken within this framework in the case of the two sample problem the required calculations are shown to take a particularly simple form special consideration is given to the two sample case in which there is an inversion of the regression effect i e where the hazard functions cross at some given point both of the motivating examples are concerned with this problem computational aspects are relatively straightforward and some discussion on this is provided

hahn hausman test as a specification test abstract this paper develops a modified version of the sargan sargan j d 1958 the estimation of economic relationships using instrumental variables econometrica 26 3 393 415 restrictions and shows that it is numerically equivalent to the test statistic of hahn and hausman hahn j hausman j 2002 a new specification test for the validity of instrumental variables econometrica 70 1 163 189 up to a sign the modified sargan test is constructed such that its asymptotic distribution under the null hypothesis of correct specification is standard normal when the number of instruments increases with the sample size the equivalence result is useful in understanding what the hahn hausman test detects and its power properties

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

correcting for selective compliance in a re employment bonus experiment we propose a two stage instrumental variable estimator that is consistent if there is selective compliance in the treatment group of a randomized experiment and the outcome variable is a censored duration the estimator assumes full compliance in the control group we use the estimator to re analyze data from the illinois re employment bonus experiment

gel statistics under weak identification abstract the central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification to this end we develop pearson type test statistics based on gel implied probabilities formed from general kernel smoothed versions of the moment indicators we also modify the statistics suggested in guggenberger and smith 2008 for a general kernel smoothing function importantly for our conclusions we provide gel time series counterparts to gmm and gel conditional likelihood ratio statistics given in kleibergen 2005 and smith 2007 our analysis not only demonstrates that these statistics are asymptotically conditionally pivotal under both classical asymptotic theory and weak instrument asymptotics of stock and wright 2000 but also provides asymptotic power results in the weakly identified time series context consequently the empirical null rejection probabilities of the associated tests and thereby the coverage probabilities of the corresponding confidence regions should not be affected greatly by the strength or otherwise of identification a comprehensive monte carlo study indicates that a number of the tests proposed here represent very competitive choices in comparison with those suggested elsewhere in the literature

the asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time the log rank test derived by mantel 1966 and peto 1972 is a special case of the efficient scores test for the proportional hazards model it is used frequently in the analysis of survival duration in clinical trials where patients entering the study are assigned at random to different treatments and are followed until they either fail or the study is terminated most survival studies are designed so that the log rank test is calculated at the termination of the study however it is not unusual for the investigator to monitor the experiment periodically it would be very useful to know the joint distribution of the test statistic at different points in time in order to adjust for the effect of repeated significance testing although the joint distribution has not been derived previously sequential procedures for the analysis of survival data in clinical trials have been given by several authors including armitage 1975 pp 140 6 jones whitehead 1979 and nagelkerke hart 1980 in this paper we establish the asymptotic joint distribution of the more general efficient scores test for the proportional hazards model calculated at different points in time and indicate how this can be used for repeated significance testing

competing risks regression for stratified data for competing risks data the fine gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function however in many important applications proportional hazards may not be satisfied including multicenter clinical trials where the baseline subdistribution hazards may not be common due to varying patient populations in this article we consider a stratified competing risks regression to allow the baseline hazard to vary across levels of the stratification covariate according to the relative size of the number of strata and strata sizes two stratification regimes are considered using partial likelihood and weighting techniques we obtain consistent estimators of regression parameters the corresponding asymptotic properties and resulting inferences are provided for the two regimes separately data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified fine gray model

inference in regression models with many regressors abstract we investigate the behavior of various standard and modified f likelihood ratio l r and lagrange multiplier l m tests in linear homoskedastic regressions adapting an alternative asymptotic framework in which the number of regressors and possibly restrictions grows proportionately to the sample size when the restrictions are not numerous the rescaled classical test statistics are asymptotically chi squared irrespective of whether there are many or few regressors however when the restrictions are numerous standard asymptotic versions of classical tests are invalid we propose and analyze asymptotically valid versions of the classical tests including those that are robust to the numerosity of regressors and restrictions the local power of all asymptotically valid tests under consideration turns out to be equal the exact f test that appeals to critical values of the f distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions

quasi maximum likelihood estimation of volatility with high frequency data this paper investigates the properties of the well known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise by extending the classic asymptotic results of quasi maximum likelihood estimation when trying to estimate the integrated volatility and the variance of noise this parametric approach remains consistent efficient and robust as a quasi estimator under misspecified assumptions moreover it shares the model free feature with nonparametric alternatives for instance realized kernels while being advantageous over them in terms of finite sample performance in light of quadratic representation this estimator behaves like an iterative exponential realized kernel asymptotically comparisons with a variety of implementations of the tukey hanning2 kernel are provided using monte carlo simulations and an empirical study with the euro us dollar future illustrates its application in practice

bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models abstract this paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear iv models under weak assumptions the method provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis the method is a non studentized version of the s test of stock and wright 2000 but is implemented and analyzed differently it does not require restrictive distributional assumptions linearity of the estimated model simultaneous equations or information about whether the instruments are strong or weak it can be applied to quantile iv models that may be nonlinear and can be used to test a parametric iv model against a nonparametric alternative it provides information about the relation between the degree of weakness of the instruments and the power of the test the bound presented here holds in finite samples regardless of the strength of the instruments

generalized high dimensional trace regression via nuclear norm regularization abstract we study the generalized trace regression with a near low rank regression coefficient matrix which extends notion of sparsity for regression coefficient vectors specifically given a matrix covariate x the probability density function of the response y is f y x c y exp 1 y b where tr t x this model accommodates various types of responses and embraces many important problem setups such as reduced rank regression matrix regression that accommodates a panel of regressors matrix completion among others we estimate through minimizing empirical negative log likelihood plus nuclear norm penalty we first establish a general theory and then for each specific problem we derive explicitly the statistical rate of the proposed estimator they all match the minimax rates in the linear trace regression up to logarithmic factors numerical studies confirm the rates we established and demonstrate the advantage of generalized trace regression over linear trace regression when the response is dichotomous we also show the benefit of incorporating nuclear norm regularization in dynamic stock return prediction and in image classification

a and b stability for runge kutta methods characterizations and equivalence using a special representation of runge kutta methods w transformation simple characterizations ofa stability andb stability have been obtained in 9 8 7 in this article we will make this representation and their conclusions more transparent by considering the exact runge kutta method finally we demonstrate by a numerical example that for difficult problemsb stable methods are superior to methods which are only a stable

many ivs estimation of dynamic panel regression models with measurement error abstract in this paper we investigate a dynamic linear panel regression model with measurement error we consider the panel data estimation whose time dimension t is not small and comparable to the cross sectional dimension n first we show that the 2sls estimator suffers from the bias problem due to many instrumental variables using the alternative asymptotics where t 3 n goes to a constant as n t we characterize its asymptotic bias due to many ivs as a bias reduction method we investigate the jive and derive its limiting distribution under the alternative asymptotics

jackknife model averaging for quantile regressions abstract in this paper we consider model averaging for quantile regressions qr when all models under investigation are potentially misspecified and the number of parameters is diverging with the sample size to allow for the dependence between the error terms and regressors in the qr models we propose a jackknife model averaging jma estimator which selects the weights by minimizing a leave one out cross validation criterion function and demonstrate its asymptotic optimality in terms of minimizing the out of sample final prediction error we conduct simulations to demonstrate the finite sample performance of our estimator and compare it with other model selection and averaging methods we apply our jma method to forecast quantiles of excess stock returns and wages

the dichotomy of stiffness pragmatism versus theory the problem of stiffness occuring in ordinary differential equations is now well understood and various concepts such as nonlinear stability b convergence and stiff order have been introduced as being relevant to an understanding of the behaviour of numerical methods when applied to stiff problems however it is often the case that some of these properties are not always attainable when methods are implemented efficiently and in this paper we will investigate this paradox in some detail in addition we will give a resume of some of the recent theoretical developments in the applicability of numerical methods to stiff problems and make some comparisons between existing codes based on runge kutta and linear multistep methods we will conclude this discussion with the introduction of a very general family of methods called multivalue methods and show how the important concepts of cheap implementation stage order and stability apply to these methods

the role of orthogonal polynomials in numerical ordinary differential equations abstract orthogonal polynomials have many applications to numerical ordinary differential equations some of these especially those connected with the quadrature formulae on which many differential equation methods are based are to be expected on the other hand there are many surprising applications quite unlike traditional uses of orthogonal polynomials this paper surveys many of these applications especially those related to accuracy and implementability of runge kutta methods

hybrid generalized empirical likelihood estimators instrument selection with adaptive lasso in this paper we use the adaptive lasso estimator to choose the relevant instruments and eliminate the irrelevant instruments the limit theory of zou 2006 is extended from univariate iid case to heteroskedastic and non gaussian data then we use the selected instruments in generalized empirical likelihood estimators gel in this sense these are called hybrid gel it is also shown that the lasso estimators are not model selection consistent whereas the adaptive lasso can select the correct model with fixed number of instruments in simulations we show that hybrid gel estimators have smaller bias and mean squared error than the other estimators in certain cases

robust standard errors in transformed likelihood estimation of dynamic panel data models with cross sectional heteroskedasticity abstract this paper extends the transformed maximum likelihood approach for estimation of dynamic panel data models by hsiao et al 2002 to the case where the errors are cross sectionally heteroskedastic this extension is not trivial due to the incidental parameters problem and its implications for estimation and inference we approach the problem by working with a mis specified homoskedastic model and then show that the transformed maximum likelihood estimator continues to be consistent even in the presence of cross sectional heteroskedasticity we also obtain standard errors that are robust to cross sectional heteroskedasticity of unknown form by means of monte carlo simulations we investigate the finite sample behavior of the transformed maximum likelihood estimator and compare it with various gmm estimators proposed in the literature simulation results reveal that in terms of median absolute errors and accuracy of inference the transformed likelihood estimator outperforms the gmm estimators in almost all cases

constructing optimal instruments by first stage prediction averaging this paper considers model averaging as a way to construct optimal instruments for the two stage least squares 2sls limited information maximum likelihood liml and fuller estimators in the presence of many instruments we propose averaging across least squares predictions of the endogenous variables obtained from many different choices of instruments and then use the average predicted value of the endogenous variables in the estimation stage the weights for averaging are chosen to minimize the asymptotic mean squared error of the model averaging version of the 2sls liml or fuller estimator this can be done by solving a standard quadratic programming problem

theoretical characteristics of the vibration of sandwich plates with in plane negative poisson s ratio values abstract this paper is concerned with re entrant cell honeycombs which show in plane negative poisson s ratio values in which their anisotropic mechanical properties are described using the cellular material theory out of plane shear moduli are affected by the unit cell geometric parameters and for some ranges of the latter it is possible to obtain higher values of the shear moduli compared to those of a regular hexagonal honeycomb in particular for cell geometries with a negative poisson s ratio a first order sandwich plate theory is applied in order to obtain the fundamental frequencies of sandwich laminates in cylindrical bending and for the simply supported case sensitivities of the frequencies per unit mass versus the geometric cell parameters are also calculated the results suggest that the dynamic performance of a sandwich structure could be significantly improved with a proper design of the unit cell shape of the honeycomb in particular re entrant cell cores offer improvements in bending stiffness capabilities for particular cell parameter ranges

robust estimation with many instruments abstract linear instrumental variables models are widely used in empirical work but often associated with low estimator precision this paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator liml intuitively this optimal robust estimator combines liml with winsorization of the structural residuals and the winsorization leads to improved precision under thick tailed error distributions consistency and asymptotic normality of the estimator are established under many instruments asymptotics and a consistent variance estimator which allows for asymptotically valid inference is provided

on the orthogonal wavelet transform for model reduction synthesis of structures model reduction techniques are widely used in numerical structural dynamics to synthesize large matrix systems and perform fast computations of natural frequencies and mode shapes several new model reduction techniques have been proposed in recent years methods such as the guyan or static reduction dynamic condensation the improved reduced system irs approach or the system equivalent reduction expansion serep may be used with good results especially over low frequency ranges 1 5 while the guyan is based solely on the sti ness matrix reduction the serep has been shown to map exactly the mass and sti ness matrices for a desired set of modes at an arbitrary set of d o f using a dynamic condensation technique with the full modal basis of the system on the other hand the irs uses guyan reduction as an estimate of the reduction system and then makes adjustments to compensate for the inertia e ects that were ignored in the guyan process without the penalty of requiring a full eigensolution advantages of using these techniques are their relative e ciency and cost e ectiveness when compared with analysis on the full system model a disadvantage however is the approximate system descriptions that result from their use sometimes leading to serious error such methods also require skilled selection of the number and location of the reduced degrees of freedom that can make up the reduced system if the degrees of freedom that represent the reduced system are chosen improperly poor solution results will follow 4 moreover classical model reduction techniques are not appropriate for synthesizing the dynamic behaviour of structures in the middleand high frequency range or with high modal densities this fact leads the structural analyst to prepare large numerical fem models with high computational costs or to use statistical energy analysis sea methods to predict the dynamic behaviour of the structure for high frequency ranges on the other hand large nite element models are already prepared for static analysis purposes their lack of use for dynamic analysis leads to an increase of the global pre processing time which greatly consumes manpower resources the existence of a reliable condensation technique for structural middle and high frequencies would also speed up the evaluation of novel materials and structures concepts for aerospace and naval applications 6 the aim of this paper is to explore the orthogonal wavelet transform for model synthesis of structures in order to preserve the middleand high frequency spectra components only a new technique is illustrated using two simple simulated examples namely a simply supported beam and a framework structure the technique is intended as an initial step

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

constructive characterization ofa stable approximations to exp z and its connection with algebraically stable runge kutta methods all rational approximations to exp z of order 2m m denotes the maximal degree of nominator and denominator are given by a closed formula involving real parameters using the theory of order stars 9 necessary and sufficient conditions fora stability respectivelyi stability are given on the basis of this characterization relations between the concepts ofa stability and algebraic stability for implicit runge kutta methods are investigated in particular we can partly prove the conjecture that to any irreduciblea stabler z of oderp 0 there exist algebraically stable runge kutta methods of the same order withr z as stability function

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

generalized hypergeometric function solutions for transverse vibration of a class of non uniform annular plates free vibration analysis of thin annular plate with thickness varying monotonically in arbitrary power form is presented transformation of variable is introduced to translate the governing equation for the free vibration of thin annular plate into a fourth order generalized hypergeometric equation the analytical solutions in terms of generalized hypergeometric function taking either logarithmic or non logarithmic forms are proposed which encompass existing published solutions as special cases to illustrate the use of the closed form solutions presented free vibration analyses of a thin annular ultra high molecular weight polyethylene and a steel plate with linear and nonlinear thickness variation are performed the results are compared with those from fe analysis based on kirchhoff thin plate theory and 3d elasticity theory indicating good agreement

construction of runge kutta type methods for solving ordinary differential equations in this paper we study runge kutta methods with continuous stage introduced by butcher in 1987 by setting the coefficients of this family of methods and choosing the appropriate numerical integration we derive new classes of runge kutta methods furthermore we extend the w transformation technique by permitting w to be a non square matrix this allows us to construct more high order implicit runge kutta methods with some geometric properties specially we provide runge kutta methods with continuous stage which are conjugate symplectic symmetric or energy preserving for solving hamiltonian systems we also present some numerical experiments to verify our results

on the stability of volterra runge kutta methods we investigate the stability of extended runge kutta methods for volterra integral equations of the second kind as test equations we choose linear convolution equations with positive definite l 1 kernels our results are strongly connected with the contractivity of runge kutta methods for nonlinear dissipative differential equations

a parallelizable preconditioner for the iterative solution of implicit runge kutta type methods the main diculty in the implementation of most standard implicit runge kutta irk methods applied to sti ordinary dierential equations odes is to eciently solve the nonlinear system of equations in this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit euler method the preconditioner is based on the w transformation of the rk coecient matrices discovered by hairer and wanner for sti odes the preconditioner is by construction asymptotically exact for methods with an invertible rk coecient matrix the methodology is particularly useful when applied to super partitioned additive runge kutta spark methods the nonlinear system can be solved by inexact simplied newton iterations at each simplied newton step the linear system can be approximately solved by an iterative method applied to the preconditioned linear system c 1999 published by elsevier science b v all rights reserved

consistent estimation with many moment inequalities in this paper we consider estimation of the identified set when the number of moment inequalities is large relative to sample size possibly infinite many applications in the recent literature on partially identified problems have this feature including dynamic games set identified iv models and parameters defined by a continuum of moment inequalities in particular conditional moment inequalities we provide a generic consistency result for criterion based estimators using an increasing number of unconditional moment inequalities we then develop more specific results for set estimation subject to conditional moment inequalities we first derive the fastest possible rate for estimating the sharp identification region under smoothness conditions on the conditional moment functions we also give rate conditions for inference under local alternatives

feasibility and contractivity in implicit runge kutta methods abstract this paper is concerned with implicit runge kutta methods for the numerical solution of initial value problems in ordinary differential equations for these methods a review is presented of the fundamental concept of algebraic stability introduced in 1979 independently by burrage butcher and by crouzeix furthermore a new framework is given in which algebraic stability becomes equivalent to both contractivity and feasibility of a runge kutta method

information in generalized method of moments estimation and entropy based moment selection abstract in this paper we make five contributions to the literature on information and entropy in generalized method of moments gmm estimation first we introduce the concept of the long run canonical correlations lrccs between the true score vector and the moment function f v t 0 and show that they provide a metric for the information contained in the population moment condition e f v t 0 0 second we show that the entropy of the limiting distribution of the gmm estimator can be written in terms of these lrccs third motivated by the above results we introduce an information criterion based on this entropy that can be used as a basis for moment selection fourth we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification fifth we analyse the behaviour of the aforementioned entropy based moment selection method in two scenarios of interest these scenarios are i nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered ii linear static models where the parameter vector may be weakly identified for some of the combinations considered the first of these contributions rests on a generalized information equality that is proved in the paper and may be of interest in its own right

the many weak instruments problem and mendelian randomization instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure we describe several techniques to reduce this bias and estimate corrected standard errors we present our findings using a simulation study and an empirical application for the latter we estimate the effect of height on lung function using genetic variants as instruments for height our simulation study demonstrates that using many weak individual variants two stage least squares 2sls is biased whereas the limited information maximum likelihood liml and the continuously updating estimator cue are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments our illustrative empirical example uses data on 3631 children from england we used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2sls liml and cue instrumental variable estimators using the individual height variants we further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments in conclusion the allele scores and cue gave consistent estimates of the causal effect in our empirical example estimates using the allele score were more efficient cue with corrected standard errors however provides a useful additional statistical tool in applications with many weak instruments the cue may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly 2014 the authors statistics in medicine published by john wiley sons ltd

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail