efficient semiparametric estimation via moment restrictions conditional moment restrictions can be combined through gmm estimation to construct more efficient semiparametric estimators this paper is about attainable efficiency for such estimators we define and use a moment tangent set the directions of departure from the truth allowed by the moments to characterize when the semiparametric efficiency bound can be attained the efficiency condition is that the moment tangent set equals the model tangent set we apply these results to transformed censored and truncated regression models e g finding that the conditional moment restrictions from powell s 1986 censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors

simple resampling methods for censored regression quantiles abstract powell journal of econometrics 25 1984 303 325 journal of econometrics 32 1986 143 155 considered censored regression quantile estimators the asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably the difficulty may be avoided by applying the bootstrap method hahn econometric theory 11 1995 105 121 calculation of the estimators however requires solving a nonsmooth and nonconvex minimization problem resulting in high computational costs in implementing the bootstrap we propose in this paper computationally simple resampling methods by convexfying powell s approach in the resampling stage a major advantage of the new methods is that they can be implemented by efficient linear programming simulation studies show that the methods are reliable even with moderate sample sizes

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

censored quantile regression with partially functional effects quantile regression offers a flexible approach to analyzing survival data allowing each covariate effect to vary with quantiles in practice constancy is often found to be adequate for some covariates in this paper we study censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects such a model can offer a simpler view regarding covariate survival association and moreover can enable improvement in estimation efficiency we propose profile estimating equations and present an iterative algorithm that can be readily and stably implemented asymptotic properties of the resultant estimators are established a simple resampling based inference procedure is developed and justified extensive simulation studies demonstrate efficiency gains of the proposed method over a naive two stage procedure the proposed method is illustrated via an application to a recent renal dialysis study

an adapted loss function for censored quantile regression in this article we study a novel approach for the estimation of quantiles when facing potential right censoring of the responses contrary to the existing literature on the subject the adopted st

exact computation of censored least absolute deviations estimator abstract we show that exact computation of the censored least absolute deviations clad estimator proposed by powell 1984 may be achieved by formulating the estimator as a linear mixed integer programming mip problem with disjunctive constraints we apply our approach to three previously studied datasets and find that widely used approximate optimization algorithms can lead to erroneous conclusions extensive simulations confirm that mip based computation using available solvers is effective for datasets typically encountered in econometric applications and that despite the proliferation of competitors clad remains a useful estimator

quantile regression for duration models with time varying regressors abstract since the seminal work of koenker and bassett 1978 quantile regression has become a widely used tool in duration analysis the existing literature however has focused on time invariant regressors even though time varying regressors are common in practice in this paper we introduce a quantile regression framework with time varying regressors and develop quantile regression estimators our estimators are motivated by manski s 1975 1985 maximum score estimator and chen s 2010 integrated maximum score estimator our estimators are consistent and asymptotically normal under some regularity conditions and perform well in finite samples our method is illustrated with an unemployment duration data set

censored regression quantiles using quantile regression to analyze survival times offers an valuable complement to traditional cox proportional hazards modelling unfortunately this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the kaplan meier estimator and applies under standard assumptions for censored regression models here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the kaplan meier estimator specifically the asymptotic behavior is directly analogous to that of the kaplan meier estimator and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case some preliminary examples suggest the strong potential of these methods as a complement to the use of cox models

pairwise difference estimators of censored and truncated regression models abstract this paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i i d and independent of the covariates the estimators exploit the fact that for a pair of observations a particular transformation of the censored variables depending upon the parameter vector and both covariate vectors will be identically distributed therefore the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector an analogous class of estimators for the truncated regression model includes the bhattacharya chernoff and yang 1983 estimator as a special case the estimators are defined as minimizers of u processes so the large sample theory for classical m estimators is extended to this case conditions are given to ensure root n consistency and asymptotic normality of the estimators and a small scale simulation study for the censored regression estimator suggest that it will be well behaved in finite samples

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

optimal smoothing in nonparametric conditional quantile derivative function estimation abstract marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles in this paper we propose a data driven bandwidth selection procedure based on the gradient of an unknown quantile regression function our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known the results of monte carlo simulations are reported and the finite sample performance of our proposed method confirms our theoretical analysis an empirical application is also provided showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method

transformed dynamic quantile regression on censored data we propose a class of power transformed linear quantile regression models for time to event observations subject to censoring by introducing a process of power transformation with different transf

estimation of the effect of numerical integration in finite element eigenvalue approximation finite element approximations of the eigenpairs of differential operators are computed as eigenpairs of matrices whose elements involve integrals which must be evaluated by numerical integration the effect of this numerical integration on the eigenvalue and eigenfunction error is estimated specifically for 2nd order selfadjoint eigenvalue problems we show that finite element approximations with quadrature satisfy the well known estimates for approximations without quadrature provided the quadrature rules have appropriate degrees of precision

on a variational approximation method for a class of elliptic eigenvalue problems in composite structures we consider a second order elliptic eigenvalue problem on a convex polygonal domain divided in m nonoverlapping subdomains the conormal derivative of the unknown function is continuous on the interfaces while the function itself is discontinuous we present a general finite element method to obtain a numerical solution of the eigenvalue problem starting from a nonstandard formally equivalent variational formulation in an abstract setting in product hilbert spaces we use standard lagrange finite element spaces on the subdomains moreover the bilinear forms are approximated by suitable numerical quadrature formulas we obtain error estimates for both the eigenfunctions and the eigenvalues allowing for the case of multiple exact eigenvalues by a pure variational method

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

bayesian averaging prediction and nonnested model selection abstract this paper studies the asymptotic relationship between bayesian model averaging and post selection frequentist predictors in both nested and nonnested models we derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples this result depends crucially on the relation between posterior odds and frequentist model selection criteria weak conditions are given under which consistent model selection is feasible regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not in the sense that they select the best model with the least number of parameters with probability converging to 1 under these conditions bayesian posterior odds and bics are consistent for selecting among nested models but are not consistent for selecting among nonnested models and possibly overlapping models these findings have important bearing for applied researchers who are frequent users of model selection tools for empirical investigation of model predictions

inference for censored quantile regression models in longitudinal studies we develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants we consider a semi parametric quantile regression model that makes no distributional assumptions our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit in such studies the focus is often on testing hypotheses about treatment equality to this end we propose a rank score test for large sample inference on a subset of the covariates we demonstrate the importance of accounting for both censoring and intra subject dependency and evaluate the performance of our proposed methodology in a simulation study we then apply the proposed inference procedures to data from an aids related clinical trial we conclude that our framework and proposed methodology is very valuable for differentiating the influences of predictors at different locations in the conditional distribution of a response variable

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

quantile regression analysis of censored longitudinal data with irregular outcome dependent follow up in many observational longitudinal studies the outcome of interest presents a skewed distribution is subject to censoring due to detection limit or other reasons and is observed at irregular times that may follow a outcome dependent pattern in this work we consider quantile regression modeling of such longitudinal data because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate outcome relationships specifically we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome such a model is easy to interpret and can accommodate dynamic outcome profile changes over time we propose estimation and inference procedures that can appropriately account for censoring and irregular outcome dependent follow up our proposals can be readily implemented based on existing software for quantile regression we establish the asymptotic properties of the proposed estimator including uniform consistency and weak convergence extensive simulations suggest good finite sample performance of the new method we also present an analysis of data from a long term study of a population exposed to polybrominated biphenyls pbb which uncovers an inhomogeneous pbb elimination pattern that would not be detected by traditional longitudinal data analysis

estimation of a nonparametric censored regression model with an application to unemployment insurance spells in this paper we consider identification and estimation of a censored nonparametric location scale model we first show that in the case where the location function is strictly less than the fixed censoring point for all values in the support of the explanatory variables then the location function is not identified anywhere in contrast if the location function is greater or equal to the censoring point with positive probability then the location function is identified on the entire support including the region where the location function is below the censoring point in the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles the new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution a small scale simulation study indicates that the proposed estimation procedure performs well in finite samples we also present an empirical application to unemployment insurance duration using administrative level data from new jersey jel classification c14 c24 j64 j65

finite element approximation for 2nd order elliptic eigenvalue problems with nonlocal boundary or transition conditions in this paper we use two symplectic schemes to simulate the ablowitz ladik model associated to the cubic nonlinear schrodinger equation and we compare them with nonsymplectic methods

a direct approach to inference in nonparametric and semiparametric quantile models we construct a generic confidence interval for a conditional quantile via the direct approach it avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile any conditional quantile estimator and any data structure provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator we also construct a generic confidence band for the conditional quantile function across a range of covariate values by using yang stute estimator and two semiparametric quantile functions we demonstrate the flexibility and simplicity of the direct approach the advantages of our new confidence intervals are borne out in a simulation study

further improvements in the calculation of censored quantile regressions censored quantile regressions of powell 1984 1986 are very powerful inferencing tools in economics and engineering as the calculation of censored quantile regressions involves minimizing a nonconvex and nondifferentiable function global optimization techniques can be the only breakthroughs the first implementation of a global optimization technique namely threshold accepting of fitzenberger and winker 1998 2007 is challenged by the genetic algorithm ga in this paper the results show that the ga provides substantial improvements over threshold accepting for cases with randomly distributed censoring points

a lagrangian method for the shallow water equations based on a voronoi mesh one dimensional results abstract a lagrangian method for the shallow water equations in one dimension is presented the method is based on the following idea place n points on a line to represent the fluid each point represents all the fluid that is closer to this point than to any other this partitions the line into intervals the principle of least action yields a set of difference equations which can be easily solved at each time step to give new values for the height and velocity of the fluid particles in each interval the points are then moved to their new locations and the intervals reconstructed in the event that two points get too close to each other consider the points to have collided the collision is treated as an inelastic collision and the two points are merged into one according to certain conservation laws it is then possible to handle flows with shocks by modelling a shock as a collision between two particles that is a shock is thought of as one fluid particle overtaking another one and colliding with it the results of this method on the dam breaking problem are presented the solution is compared to the exact solution and to a solution by the random choice method

spectral element approximation of fredholm integral eigenvalue problems we consider the numerical approximation of homogeneous fredholm integral equations of second kind with emphasis on computing truncated karhunen loeve expansions we employ the spectral element method with gauss lobatto legendre gll collocation points similar to the piecewise constant finite elements this approach is simple to implement and does not lead to generalized discrete eigenvalue problems numerical experiments confirm the expected convergence rates for some classical kernels and illustrate how this approach can improve the finite element solution of partial differential equations with random input data

lumped mass matrix in explicit finite element method for transient dynamics of elasticity abstract the mass matrix of structural dynamics is discussed for the approximations by linear elements with constant jacobians the a priori error estimate is derived for the explicit finite element method using diagonal mass matrix with smooth solutions it is shown that by using diagonal mass matrix or consistent mass matrix the displacement velocity and the energies have the same convergence rates in fact the difference in numerical errors by these two methods is of order h2 the same conclusion is valid for a certain type of reissner mindlin plate element for transient dynamics

mesh duality and legendre duality we describe a sense in which mesh duality is equivalent to legendre duality that is a general pair of meshes which satisfy a definition of duality for meshes are shown to be the projection of a pair of piecewise linear functions that are dual to each other in the sense of a legendre dual transformation in applications the latter functions can be a tangent plane approximation to a smoother function and a chordal plane approximation to its legendre dual convex examples include one from meteorology and also the relation between the delaunay mesh and the voronoi tessellation the latter are shown to be the projections of tangent plane and chordal approximations to the same paraboloid

the consistency of nonlinear regression minimizing the l_1 norm we consider conditions in a nonlinear regression model for the consistency of the estimator obtained by minimizing the l 1 norm i e the sum of absolute deviations

about the delaunay voronoi tesselation abstract the topological description of the neighborhood of the constituing atoms in a dense random material liquids glasses is of a major importance for their characterization we discuss an algorithm for the delaunay construction which is global and independent of the dimension of the space and derive from it the full dual voronoi tesselation by an original realization of duality

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

dual variables in semigeostrophic theory this paper is a study of the duality structure present in the semigeostrophic equations of meterology we explore a new viewpoint represented by legendre transformations between alternative choices of independent variables including space coordinates geostrophic coordinates and isentropic coordinates detailed examples are given for both uniform and non uniform potential vorticity of the modelling of an atmospheric front at a given time in stable flow in each case the front is a half line of gradient discontinuity on a continuous convex surface obtained as the self intersection on a swallowtail surface after the latter is convexified so that non physical multivaluedness is removed

conditional empirical likelihood estimation and inference for quantile regression models abstract this paper considers two empirical likelihood based estimation inference and specification testing methods for quantile regression models first we apply the method of conditional empirical likelihood cel by kitamura et al 2004 empirical likelihood based inference in conditional moment restriction models econometrica 72 1667 1714 and zhang and gijbels 2003 sieve empirical likelihood and extensions of the generalized least squares scandinavian journal of statistics 30 1 24 to quantile regression models second to avoid practical problems of the cel method induced by the discontinuity in parameters of cel we propose a smoothed counterpart of cel called smoothed conditional empirical likelihood scel we derive asymptotic properties of the cel and scel estimators parameter hypothesis tests and model specification tests important features are i the cel and scel estimators are asymptotically efficient and do not require preliminary weight estimation ii by inverting the cel and scel ratio parameter hypothesis tests asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators and iii in contrast to cel the scel method can be implemented by some standard newton type optimization simulation results demonstrate that the scel method in particular compares favorably with existing alternatives

a finite element method for differential eigenvalue problems with mixed classical and semi periodic boundary conditions this paper deals with a class of elliptic eigenvalue problems evps for second order differential equations des on a rectangular domain email protected r 2 with periodic or semi periodic boundary conditions bcs on two opposite sides of w on the remaining sides classical robin or dirichlet type bcs are imposed this type of evp is given a suitable variational formulation which allows us to recast the evp in the framework of abstract evps for symmetric bounded coercive bilinear forms in hilbert spaces leading to the existence of exact eigenpairs from the other side the variational evp serves as the starting point for finite element methods without and with numerical quadrature both triangular and rectangular meshes are considered moreover we allow for the case of multiple exact eigenvalues well known error estimates established for finite element approximations of elliptic evps with classical bcs are shown to remain valid for the present type of evp too some attention is also paid to the computational aspects of the resulting algebraic evp finally the analysis is illustrated by a numerical example

adaptivity techniques for compressible inviscid flows abstract to enhance the resolution of numerically simulated flowfields grid adaptivity is vitally important further to afford complete flexibility in the spatial discretisation of the flow domain both structured unstructured and combinations of grid types are likely to be required hence the development of grid adaptivity techniques for general grids is important this paper discusses adaptivity achieved through point enrichment point derefinement and point movement applied on general grids a flexible data structure is described together with suitable strategies for adaptively refining a computational grid applications are presented of adaptive grid refinement for two dimensional compressible flow simulation

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

rates of convergence for estimating regression coefficients in heteroskedastic discrete response models abstract in this paper we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term it is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction the semiparametric information bound is zero even when the homoskedastic error term is parametrically specified hence it is impossible to attain the parametric convergence rate for the parameters of interest however for ordered response models where the response variable can take at least three different values the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption two estimation procedures are proposed the first estimator based on a parametric restriction on the homoskedastic component of the error term is a two step maximum likelihood estimators where the unknown scale function is estimated nonparametrically in the first stage the second procedure which does not require the parametric restriction estimates the parameters by a kernel weighted least squares procedure under regularity conditions which are standard in the literature both estimators are shown to be n consistent and asymptotically normal

asymptotic inference for the constrained quantile regression process abstract i investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space in order to allow for inferences made across many conditional quantiles i provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels to do this i pose the process of estimates as solutions to a parameterized family of constrained optimization problems parameterized by quantile level a uniform characterization of the dual solution to these problems the so called regression rankscore process is also derived which can be used for score type inference in quantile regression the asymptotic behavior of quasi likelihood ratio wald and regression rankscore processes for inference when the null hypothesis asserts that the parameters lie on a boundary follows from the features of the constrained solutions

bagging binary and quantile predictors for time series abstract bootstrap aggregating or bagging introduced by breiman 1996a bagging predictors machine learning 24 123 140 has been proved to be effective to improve on unstable forecast theoretical and empirical works using classification regression trees variable selection in linear and non linear regression have shown that bagging can generate substantial prediction gain however most of the existing literature on bagging has been limited to the cross sectional circumstances with symmetric cost functions in this paper we extend the application of bagging to time series settings with asymmetric cost functions particularly for predicting signs and quantiles we use quantile predictions to construct a binary predictor and the majority voted bagging binary prediction we show that bagging may improve the binary prediction in small sample but it does not improve in large sample various bagging forecast combination weights are used such as equal weighted and bayesian model averaging bma weighted combinations for demonstration we present results from monte carlo experiments and from empirical applications using monthly s p500 and nasdaq stock index returns

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

quasi likelihood for median regression models abstract this article proposes quasi likelihood equations for median regression models the quasi likelihood can be used for dependent observations such as repeated measurements or time series data to construct a quasi likelihood equation we need to specify the relation between the median and the dispersion and also specify the dependency of the observations if a monotone transformation of the original observation has a laplace distribution then the quasi likelihood is the exact likelihood under moderate assumptions the quasi likelihood estimates are consistent and have asymptotically normal distributions the estimates are also shown to have minimal asymptotic variance within a certain class of consistent estimates the proposed method is illustrated using data from a clinical trial

endogeneity in quantile regression models a control function approach this paper considers a linear triangular simultaneous equations model with conditional quantile restrictions the paper adjusts for endogeneity by adopting a control function approach and presents a simple two step estimator that exploits the partially linear structure of the model the first step consists of estimation of the residuals of the reduced form equation for the endogenous explanatory variable the second step is series estimation of the primary equation with the reduced form residual included nonparametrically as an additional explanatory variable this paper imposes no functional form restrictions on the stochastic relationship between the reduced form residual and the disturbance term in the primary equation conditional on observable explanatory variables the paper presents regularity conditions for consistency and asymptotic normality of the two step estimator in addition the paper provides some discussions on related estimation methods in the literature and on possible extensions and limitations of the estimation approach finally the numerical performance and usefulness of the estimator are illustrated by the results of monte carlo experiments and two empirical examples demand for fish and returns to schooling

estimating the asymptotic covariance matrix for quantile regression models a monte carlo study abstract this monte carlo study examines several estimation procedures of the asymptotic covariance matrix in the quantile and censored quantile regression models design matrix bootstrap error bootstrapping order statistic sigma bootstrap homoskedastic kernel and heteroskedastic kernel the monte carlo samples are drawn from two alternative data sets 1 a the unaltered current population survey cps for 1987 and 2 b this cps data with independence between error term and regressors imposed this special setup allows one to evaluate the estimators under various realistic scenarios the results favor the design bootstrap for the general case but also support the order statistic when the error term is independent of the regressors

competing risks quantile regression quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized in this paper we study quantile regression with competing risks data formulating the model based on conditional quantiles defined using the cumulative incidence function which includes as a special case an analog to the usual accelerated failure time model the proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and moreover relaxes the constancy constraint on regression coefficients thereby providing a useful perhaps more flexible alternative to the popular subdistribution proportional hazards model we derive an unbiased monotone estimating equation for regression parameters in the quantile model the uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum we develop inferences including covariance estimation second

solvency supervision based on a total balance sheet approach in this paper we investigate the adequacy of the own funds a company requires in order to remain healthy and avoid insolvency two methods are applied here the quantile regression method and the method of mixed effects models quantile regression is capable of providing a more complete statistical analysis of the stochastic relationship among random variables than least squares estimation the estimated mixed effects line can be considered as an internal industry equation norm which explains a systematic relation between a dependent variable such as own funds with independent variables e g financial characteristics such as assets provisions etc the above two methods are implemented with two data sets

censored regression quantiles with endogenous regressors this paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous and continuously distributed and instrumental variables are available for them a distributional exclusion restriction is imposed on the unobservable errors whose conditional distribution is assumed to depend on the regressors and instruments only through a lower dimensional control variable here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments this assumption which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable is used to motivate a two stage estimator of the censored regression coefficients in the first stage the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated as are the first stage reduced form residuals to be used as control variables the second stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors using only pairs of observations for which both estimated quantiles are positive i e in the uncensored region and the corresponding difference in estimated control variables is small the paper gives the form of the asymptotic distribution for the proposed estimator and discusses how it compares to similar estimators for alternative models

mirror symmetry via logarithmic degeneration data i this paper lays the foundations of a program to study mirror symmetry by studying the log structures of illusie fontaine and kato on degenerations of calabi yau manifolds the basic idea is that one can associate to certain sorts of degenerations of calabi yau manifolds a log calabi yau space which is a log structure on the degenerate fibre the log cy space captures essentially all the information of the degeneration and hence all mirror statements for the large complex structure limit given by the degeneration can already be derived from the log cy space in this paper we begin by discussing affine manifolds with singularities given such an affine manifold along with a polyhedral decomposition we show how to construct a scheme consisting of a union of toric varieties in certain non degenerate cases we can also construct log structures on these schemes conversely given certain sorts of degenerations one can build an affine manifold with singularities structure on the dual intersection complex of the degeneration mirror symmetry is then obtained as a discrete legendre transform on these affine manifolds thus providing an algebro geometrization of the strominger yau zaslow conjecture the deepest result of this paper shows an isomorphism between log complex moduli of a log cy space and log kahler moduli of its mirror

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

multiple imputation for m regression with censored covariates we develop a new multiple imputation approach for m regression models with censored covariates instead of specifying parametric likelihoods our method imputes the censored covariates by their conditional quantiles given the observed data where the conditional quantiles are estimated through fitting a censored quantile regression process the resulting estimator is shown to be consistent and asymptotically normal and it improves the estimation efficiency by using information from cases with censored covariates compared with existing methods the proposed method is more flexible as it does not require stringent parametric assumptions on the distributions of either the regression errors or the covariates the finite sample performance of the proposed method is assessed through a simulation study and the analysis of a c reactive protein dataset in the 2007 2008 national health and nutrition examination survey this article has supplementary material online

estimation of high conditional quantiles for heavy tailed distributions estimation of conditional quantiles at very high or low tails is of interest in numerous applications quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution however high tails are often associated with data sparsity so quantile regression estimation can suffer from high variability at tails especially for heavy tailed distributions in this article we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors we establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates in a real application involving statistical downscaling of daily precipitation in

some results in lumped mass finite element approximation of eigenvalue problems using numerical quadrature formulas in this paper we establish the convergence and the rate of convergence for approximate eigenvalues and eigenfunctions of second order elliptic eigenvalue problems obtained by a lumped mass finite element approximation various aspects of lumped mass techniques have been discussed for such eigenvalue problems by fix 1972 ishihara 1977 strang and fix 1973 and tong et al 1971 among others in our approach the lumping of the mass matrix results from the use of a lobatto quadrature formula for the integrals over rectangular lagrange finite elements of degree k

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

multiple imputation for cure rate quantile regression with censored data summary the main challenge in the context of cure rate analysis is that one never knows whether censored subjects are cured or uncured or whether they are susceptible or insusceptible to the event of interest considering the susceptible indicator as missing data we propose a multiple imputation approach to cure rate quantile regression for censored data with a survival fraction we develop an iterative algorithm to estimate the conditionally uncured probability for each subject by utilizing this estimated probability and bernoulli sample imputation we can classify each subject as cured or uncured and then employ the locally weighted method to estimate the quantile regression coefficients with only the uncured subjects repeating the imputation procedure multiple times and taking an average over the resultant estimators we obtain consistent estimators for the quantile regression coefficients our approach relaxes the usual global linearity assumption so that we can apply quantile regression to any particular quantile of interest we establish asymptotic properties for the proposed estimators including both consistency and asymptotic normality we conduct simulation studies to assess the finite sample performance of the proposed multiple imputation method and apply it to a lung cancer study as an illustration

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

logistic quantile regression for bounded outcomes when research interest lies in continuous outcome variables that take on values within a known range e g a visual analog scale for pain within 0 and 100 mm the traditional statistical methods such as least squares regression mixed effects models and even classic nonparametric methods such as the wilcoxon s test may prove inadequate frequency distributions of bounded outcomes are often unimodal u shaped and j shaped to the best of our knowledge in the biomedical and epidemiological literature bounded outcomes have seldom been analyzed by appropriate methods that for one correctly constrain inference to lie within the feasible range of values in many respects continuous bounded outcomes can be likened to probabilities or propensities yet what has long been heeded when modeling the probability of binary outcomes with the widespread use of logistic and probit regression so far appears to have been overlooked with continuous bounded outcomes with consequences at times disastrous logistic quantile regression constitutes an effective method to fill this gap

spectral element computation of high frequency leaky modes in three dimensional solid waveguides a numerical method is proposed to compute high frequency low leakage modes in structural waveguides surrounded by infinite solid media in order to model arbitrary shape structures a waveguide formulation is used which consists of applying to the elastodynamic equilibrium equations a space fourier transform along the waveguide axis and then a discretization method to the cross section coordinates however several numerical issues must be faced related to the unbounded nature of the cross section the number of degrees of freedom required to achieve an acceptable error in the high frequency regime as well as the number of modes to compute in this paper these issues are circumvented by applying perfectly matched layers pml along the cross section directions a high order spectral element method for the discretization of the cross section and an eigensolver shift suited for the computation of low leakage modes first computations are performed for an embedded cylindrical bar for which literature results are available the proposed pml waveguide formulation yields good agreement with literature results even in the case of weak impedance contrast its performance with high order spectral elements is assessed in terms of convergence and accuracy and compared to traditional low order finite elements then computations are performed for an embedded square bar dispersion curves exhibit strong similarities with cylinders these results show that the properties of low leakage modes observed in cylindrical bars can also occur in other types of geometry

extremal quantile regression quantile regression is an important tool for estimation of conditional quantiles of a response y given a vector of covariates x it can be used to measure the effect of covariates not only in the center of a distribution but also in the upper and lower tails this paper develops a theory of quantile regression in the tails specifically it obtains the large sample properties of extremal extreme order and intermediate order quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values this modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis in large samples extreme order regression quantiles converge weakly to arg min functionals of stochastic integrals of poisson processes that depend on regressors while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design

median regression with censored cost data because of the skewness of the distribution of medical costs we consider modeling the median as well as other quantiles when establishing regression relationships to covariates in many applications the medical cost data are also right censored in this article we propose semiparametric procedures for estimating the parameters in median regression models based on weighted estimating equations when censoring is present numerical studies are conducted to show that our estimators perform well with small samples and the resulting inference is reliable in circumstances of practical importance the methods are applied to a dataset for medical costs of patients with colorectal cancer

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

quantile regression for left truncated semicompeting risks data summary semicompeting risks is often encountered in biomedical studies where a terminating event censors a nonterminating event but not vice versa in practice left truncation on the terminating event may arise and can greatly complicate the regression analysis on the nonterminating event in this work we propose a quantile regression method for left truncated semicompeting risks data which provides meaningful interpretations as well as the flexibility to accommodate varying covariate effects we develop estimation and inference procedures that can be easily implemented by existing statistical software asymptotic properties of the resulting estimators are established including uniform consistency and weak convergence the finite sample performance of the proposed method is evaluated via simulation studies an application to a registry dataset provides an illustration of our proposals

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples

quantile regression adjusting for dependent censoring from semicompeting risks in this work we study quantile regression when the response is an event time subject to potentially dependent censoring we consider the semi competing risks setting where time to censoring remains observable after the occurrence of the event of interest while such a scenario frequently arises in biomedical studies most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent by imposing rather mild assumptions on the association structure between the time to event response and the censoring time variable we propose quantile regression procedures which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring an efficient and stable algorithm is provided for implementing the new method we establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence the theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals extensive simulation studies suggest that the proposed method performs well with moderate sample sizes we illustrate the practical utility of our proposals through an application to a bone marrow transplant trial

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package

on the construction of the voronoi mesh on a sphere abstract a new construction of the voronoi mesh on the sphere is presented the main feature is that the algorithm adds points one at a time until the final voronoi mesh is built up by adding one point to an existing voronoi mesh of k points only local changes are needed to construct a voronoi mesh of k 1 points this construction is particularly well suited to time dependent problems since using information from the voronoi mesh at the previous time step allows us to reduce the construction to o n operations when the two configurations are close while the algorithm does not break down when they are far apart numerical experiments are presented to substantiate the o n operation count for a typical case

a new algorithm for three dimensional voronoi tessellation abstract a new efficient algorithm for computing the voronoi tessellation in three dimensions is presented the voronoi tessellation is obtained by constructing delaunay tetrahedra the complete set of these tetrahedra corresponds to that of a single voronoi polyhedron

on the predictive risk in misspecified quantile regression abstract in the present paper we investigate the predictive risk of possibly misspecified quantile regression functions the in sample risk is well known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple asymptotic characterizations of the associated bias also called expected optimism we propose estimates for the expected optimism and the predictive risk and establish their uniform consistency under mild conditions our results hold for models of moderately growing size and allow the quantile function to be incorrectly specified empirical evidence from our estimates is encouraging as it compares favorably with cross validation

the parabolic umbilic and atmospheric fronts this paper describes how to calculate the legendre transformation of the beak to beak form of the parabolic umbilic the result is a multivalued surface in three dimensions with multiplicity of up to five which contains cusped edges of regression and lines of self intersection the calculation is self contained and is elementary in method but intricate in detail the ideas in it will be available in other such calculations of similar complexity and for any required context our underlying motivation is the study of atmospheric fronts in semigeostrophic theory we show how a front may be regarded as a selfintersection line terminating at a swallowtail point on the legendre transform surface a physical stability argument requires excision of certain parts of the surface to leave a jointly convex and single valued surface having a gradient discontinuity along the front a numerical illustration is presented this paper has two purposes the major part works out in detail the legendre transformation of the beak to beak form of the parabolic umbilic this calculation stands in its own right not oriented to any particular application and is addressed to a wide mathematical audience in a non committal notation the second purpose is to initiate and examine briefly a new way of studying atmospheric fronts which uses the result just obtained we explain how in suitably chosen variables a front may be regarded as terminating at a certain kind of swallowtail point qualitatively similar to one found on the legendre transform of the beak to beak potential this idea was the original motivation for the calculation mentioned above semigeostrophic theory in meteorology contains an analytical device which in fact is an example of a legendre transformation although previously unrecognized as such as remarked by sewell i987 p 157 the transformation is a certain kind of mapping from one single valued function to another function which may be multivalued in the first instance a single valued part of the latter is then retained by using arguments from atmospheric physics to delete unwanted branches for example those which represent unstable regimes the mapping which remains is from a smooth single valued convex function to another single valued convex function which is smooth everywhere except along a half line of gradient discontinuity and this half line represents the front the convexity thus retained by the physical stability argument is qualitatively similar