conditional scores and optimal scores for generalized linear measurement error models abstract this paper studies estimation of the parameters of generalized linear models in canonical form when the explanatory vector is measured with independent normal error for the functional case i e when the explanatory vectors are fixed constants unbiased score functions are obtained by conditioning on certain sufficient statistics this work generalizes results obtained for logistic regression in the case that the explanatory vectors are independent and identically distributed with unknown distribtuion efficient score functions are obtained using the theory developed in begun et al 1983 keywords conditional score function efficient score function functional model generalized linear model measurement error structural model

cure rate model with mismeasured covariates under transformation cure rate models explicitly account for the survival fraction in failure time data when the covariates are measured with errors naively treating mismeasured covariates as error free would cause estimation bias and thus lead to incorrect inference under the proportional hazards cure model we propose a corrected score approach as well as its generalization and implement a transformation on the mismeasured covariates toward error additivity and or normality the corrected score equations can be easily solved through the backfitting procedure and the biases in the parameter estimates are successfully eliminated we show that the proposed estimators for the regression coefficients are consistent and asymptotically normal we conduct simulation studies to examine the finite sample properties of the new method and apply it to a real data set for illustration

meboost variable selection in the presence of measurement error we present a novel method for variable selection in regression models when covariates are measured with error the iterative algorithm we propose measurement error boosting meboost follows a path defined by estimating equations that correct for covariate measurement error we illustrate the use of meboost in practice by analyzing data from the box lunch study a clinical trial in nutrition where several variables are based on self report and hence measured with error where we are interested in performing model selection from a large data set to select variables that are related to the number of times a subject binge ate in the last 28 days furthermore we evaluated our method and compared its performance to the recently proposed convex conditioned lasso and to the naive lasso which does not correct for measurement error through a simulation study increasing the degree of measurement error increased prediction error and decreased the probability of accurate covariate selection but this loss of accuracy occurred to a lesser degree when using meboost through simulations we also make a case for the consistency of the model selected

degrees of freedom of cache aided wireless cellular networks this work investigates the degrees of freedom dof of a downlink cache aided cellular network where the locations of base stations bss are modeled as a grid topology and users within a grid cell can only communicate with four nearby bss we adopt a cache placement method with uncoded prefetching tailored for the network with partial connectivity according to the overlapped degree of cached contents among bss we propose transmission schemes with no bs cooperation partial bs cooperation and full bs cooperation respectively for different cache sizes in specific the common cached contents among bss are utilized to cancel some undesired signals by interference neutralization while interference alignment is used to coordinate signals of distinct cached contents our achievable results indicate that the reciprocal of per user dof of the cellular network decreases piecewise linearly with the normalized cache size mu at each bs and the gain of bs caching is more significant for the small cache region under the given cache placement scheme we also provide an upper bound of per user dof and show that our achievable dof is optimal when mu in left frac 1 2 1 right and within an additive gap of frac 4 39 to the optimum when mu in left frac 1 4 frac 1 2 right

dynamical singularities for complex initial conditions and the motion at a real separatrix this work investigates singularities occurring at finite real times in the classical dynamics of one dimensional double well systems with complex initial conditions the objective is to understand the relationship between these singularities and the behavior of the systems for real initial conditions an analytical treatment establishes that the dynamics of a quartic double well system possesses a doubly infinite sequence of singularities these are associated with initial conditions that converge to those for the real separatrix as the singularity time becomes infinite this confluence of singularities is shown to lead to the unstable behavior that characterizes the real motion at the separatrix numerical calculations confirm the existence of a large number of singularities converging to the separatrix for this and two additional double well systems the approach of singularities to the real axis is of particular interest since such behavior has been related to the formation of chaos in nonintegrable systems the properties of the singular trajectories which cause this convergence to the separatrix are identified the hyperbolic fixed point corresponding to the potential energy maximum responsible for the characteristic motion at a separatrix also plays a critical role in the formation of the complex singularities by delaying trajectories and then deflecting them into asymptotic regions of space from where they are directly repelled to infinity in a finite time

similarity reductions from extended painleve expansions for nonintegrable evolution equations abstract the use of singular manifold expansions to find exact solutions to nonintegrable evolution equations is extended to include arbitrary resonance coefficients in such a way as to make the resulting infinite series exactly resummable the technique involves the use of a rescaling ansatz analogous to that used to analyze the psi series of nonintegrable ordinary differential equations the result is a similarity reduction of the equation in which the constrained singular manifold plays the role of a similarity variable the method is capable of yielding new solutions corresponding to either classical or nonclassical conditional lie symmetries

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

orthogonal locally ancillary estimating functions for matched pair studies and errors in covariates summary we propose an estimating function method for two related applications matched pair studies and studies with errors in covariates under a functional model where a mismeasured unknown scalar covariate is treated as a fixed nuisance parameter our method addresses the severe inferential problem that is posed by an abundance of nuisance parameters in these two applications we propose orthogonal locally ancillary estimating functions for these two applications that depend on merely the mean model and partial modelling of the variances of the observations and observed mismeasured covariate if applicable and we achieve first order bias correction of inferences under a small dispersion and large sample size asymptotic simulation results confirm that the estimator proposed is largely improved over that using a regular profile estimating function we apply the approach proposed to a length of hospital stay study with a mismeasured covariate

on the non integrability of a family of duffing van der pol oscillators we investigate the non integrability of a family of duffing van der pol oscillators x alpha x x2 1 x beta x3 gamma cos omega t by studying the analytic properties of the dynamics in complex time we find that the solutions of have no worse than algebraic singularities at t with only t t 1 2 terms present in their series expansions unlike for example the alpha 0 duffing case where typically log t t terms arise still when integrating around long enough contours a remarkably intricate pattern of square root singularities emerges on different sheets which appears to prevent solutions from ever returning to the original sheet such evidence of infinitely sheeted solutions termed the iss property has also been observed in a number of hamiltonian systems and is illustrated here on a simple example of a single first order differential equation we suggest that the iss property is a necessary condition for non integrability i e non existence of a complete set of analytic single valued constants of the motion which would permit the complete integration of a dynamical system in terms of quadratures

estimation of dependence between paired correlated failure times in the presence of covariate measurement error summary in many biomedical studies covariates are subject to measurement error although it is well known that the regression coefficients estimators can be substantially biased if the measurement error is not accommodated there has been little study of the effect of covariate measurement error on the estimation of the dependence between bivariate failure times we show that the dependence parameter estimator in the clayton oakes model can be considerably biased if the measurement error in the covariate is not accommodated in contrast with the typical bias towards the null for marginal regression coefficients the dependence parameter can be biased in either direction we introduce a bias reduction technique for the bivariate survival function in copula models while assuming an additive measurement error model and replicated measurement for the covariates and we study the large and small sample properties of the dependence parameter estimator proposed

non integrable systems with algebraic singularities in complex time dynamical arguments are presented which suggest that there are non integrable systems without clustering of singularities without infinite singularities or singularities with an infinite number of branches in the complex t plane several examples with only algebraic singularities are studied for which strong numerical evidence is presented for non integrability and infinitely sheeted solutions weak painleve potentials are also analysed from this point of view and all integrable cases are found to possess only finitely sheeted solutions

exact solutions of the multidimensional derivative nonlinear schrodinger equation for many body systems of criticality the authors investigate the problem of strongly interacting many body systems near criticality as recently described in terms of nonlinear dynamics by dixon and tuszynski 1989 they show that in the first order of approximation the equation of motion for the order parameter can be mapped on the derivative nonlinear schrodinger equation and thus can be solved exactly they solve the equations both in the absence and presence of current densities

on the analytic structure of the driven pendulum the analytic structure of the solution of the driven pendulum is investigated through painleve analysis in the complex time plane the existence is pointed out of a two armed infinite sheeted riemann structure of the singularities after an exponential transformation

small area estimation when auxiliary information is measured with error summary small area estimation methods typically combine direct estimates from a survey with pre dictions from a model in order to obtain estimates of population quantities with reduced mean squared error when the auxiliary information used in the model is measured with error using a small area estimator such as the fay herriot estimator while ignoring measurement error may be worse than simply using the direct estimator we propose a new small area estimator that accounts for sampling variability in the auxiliary information and derive its properties in particular show ing that it is approximately unbiased the estimator is applied to predict quantities measured in the u s national health and nutrition examination survey with auxiliary information from the u s national health interview survey

cellular interference alignment interference alignment promises that in gaussian interference channels each link can support half of a degree of freedom dof per pair of transmit receive antennas however in general this result requires to precode the data bearing signals over a signal space of asymptotically large diversity e g over an infinite number of dimensions for time frequency varying fading channels or over an infinite number of rationally independent signal levels in the case of time frequency invariant channels in this paper we consider a wireless cellular system scenario where the promised optimal dofs are achieved with linear precoding in one shot i e over a single time frequency slot we focus on the uplink of a symmetric cellular system where each cell is split into three sectors with orthogonal intrasector multiple access in our model interference is local i e it is due to transmitters in neighboring cells only we consider a noniterative local cooperation scheme where base stations pass to their neighbors their decoded messages such that interference from already decoded messages can be canceled therefore for a given decoding order the interference between sectors is described by a directed locally connected graph the problem consists of maximizing the per sector dofs over all possible decoding orders and precoding schemes in particular we provide a decoding order and a one shot interference alignment scheme able to achieve optimal per sector dofs up to an additive gap due to boundary effects that vanishes as the size of the network becomes large then we extend our treatment by considering the case of intersector interference with joint processing of the three sector at each cell site in order to avoid signaling schemes relying on the strength of interference we further introduce the notion of topologically robust schemes which are able to guarantee a minimum rate or dofs irrespectively of the strength of the interfering links toward this end we design a different decoding order and alignment scheme which is topologically robust and still achieves the same optimum dofs finally we provide a new scheme for the downlink based on local base station cooperation where base stations pass to their neighbors a quantized version of their dirty paper coded signals for the proposed downlink scheme we can prove a dofs duality result showing that for an appropriate choice of the precoding order and of the alignment beamforming vectors it can achieve the same per sector dofs of the corresponding uplink schemes

corrected score function for errors in variables models methodology and application to generalized linear models summary statistical models whose independent variables are subject to measurement errors are often referred to as errors in variables models to correct for the effects of measurement error on parameter estimation this paper considers a correction for score functions a corrected score function is one whose expectation with respect to the measurement error distribution coincides with the usual score function based on the unknown true independent variables this approach makes it possible to do inference as well as estimation of model parameters without additional assumptions the corrected score functions of some generalized linear models are obtained

investigating non integrability and chaos in complex time the question of integrability of systems of ordinary differential equations odes has been studied extensively for centuries recently however owing to an upsurge of interest in chaos a lot of studies have focused on the investigation of non integrable systems where chaos often manifests itself as extremely sensitive dependence on initial conditions of a dense set of real solutions in real time here we argue that non integrability can be efficiently investigated by solving odes in complex time and review recent results which strongly suggest that for a system of odes to be non integrable it is necessary that it possess a dense set of infinitely sheeted solutions in the complex domain

smoothed and corrected score approach to censored quantile regression with measurement errors censored quantile regression is an important alternative to the cox proportional hazards model in survival analysis in contrast to the usual central covariate effects quantile regression can effectively characterize the covariate effects at different quantiles of the survival time when covariates are measured with errors it is known that naively treating mismeasured covariates as error free would result in estimation bias under censored quantile regression we propose smoothed and corrected estimating equations to obtain consistent estimators we establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients compared with the naive estimator the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions we conduct simulation studies to examine the finite sample properties of the new method and apply it to a lung cancer study supplementary materials for this article are available online

simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models abstract we develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates we assume the model error and covariate distributions are unspecified and the measurement error distribution is a general parametric distribution with unknown variance covariance we construct root n consistent asymptotically normal and locally efficient estimators using the semiparametric efficient score we do not estimate any unknown distribution or model error heteroskedasticity instead we form the estimator under possibly incorrect working distribution models for the model error error prone covariate or both empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error prone covariates

necessary and sufficient conditions for finite time singularities in ordinary differential equations abstract this paper gives a theorem which provides necessary and sufficient conditions for the existence of a real finite value of the independent variable at which the general solution of a certain class of ordinary differential equations diverges to infinity this class is a large subset of the set of all autonomous non linear polynomial ordinary differential equation these conditions involve the asymptotic form of the local series representation for the general solutions around the singularities and can be checked algorithmically

on exact solutions for damped anharmonic oscillators for arbitrary functions f1 f2 and f3 the anharmonic oscillator x f1 t x f2 t x f3 t x3 0 cannot be solved in closed form i e the general solution cannot be expressed as elliptic functions the authors apply the painleve test to obtain the constraint on the functions f1 f2 and f3 for which the equation passes the test the constraint on f1 f2 and f3 i e the differential equation which f1 f2 and f3 obey is discussed and solutions are given

consistent functional methods for logistic regression with errors in covariates we propose consistent functional methods for logistic regression in which some covariates are not accurately ascertainable among existing methods for generalized linear models the conditional score approach to normal errors does not guarantee the convergence of its estimators and the corrected score method generally is not applicable to the logistic regression score function in this article after constructing a correction amenable estimation procedure with the true covariates we formulate parametric and nonparametric correction estimation procedures in the presence of additive errors in covariates the former procedure accommodates the situation with known but not necessarily normal error distribution whereas the latter further relieves this distributional assumption requirement given that additional replicated mismeasured covariates or instrumental variables are available large sample theory is developed the proposed estimators are consistent and asymptotically normal we investigate their a

eeboost a general method for prediction and variable selection based on estimating equations the modern statistical literature is replete with methods for performing variable selection and prediction in standard regression problems however simple models may misspecify or fail to capture important aspects of the data generating process such as missingness correlation and over underdispersion in this article we describe eeboost a strategy for variable selection and prediction which can be applied in high dimensional settings where inference for low dimensional parameters would typically be based on estimating equations the method is simple flexible and easily implemented using existing software the eeboost algorithm is obtained as a modification of the standard boosting or functional gradient descent technique we show that eeboost is closely related to a class of l1 constrained projected likelihood ratio minimizations and therefore produces similar variable selection paths to penalized methods without the need to apply constrained optimization algorithms the flexibility of eeboost is

degrees of freedom of interference channels with comp transmission and reception we study the degrees of freedom dof of the k user interference channel with coordinated multipoint comp transmission and reception each message is jointly transmitted by m t successive transmitters and is jointly received by m r successive receivers we refer to this channel as the comp channel with a transmit cooperation order of m t and receive cooperation order of m r since the channel has a total of k transmit antennas and k receive antennas the maximum possible dof is equal to k we show that the comp channel has k dof if and only if m t m r geq k 1 the key idea is that the zero forcing of the interference corresponding to the i rm th message at the decoder of the j rm th message where j ne i can be viewed as a shared responsibility between the m t transmitters carrying the i rm th message and the m r receivers decoding the j rm th message for the general case we derive an outer bound that states that the dof is bounded above by left lceil k m t m r 2 2 right rceil for the special case with only comp transmission i e m r 1 we propose a scheme that can achieve k m t 1 2 dof for all k and conjecture that the result holds true for all k in the proposed coding scheme the m t transmitters carrying each message are used to cancel the interference introduced by this message at the first m t 1 receivers thereby allowing each of these receivers to enjoy 1 dof and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space the achievability proofs are based on the notion of algebraic independence from algebraic geometry

singularity clustering in the duffing oscillator an asymptotic and numerical study is made of the singularity structure in the complex t plane of the duffing oscillator the presence of logarithmic terms in the local psi series expansion of the form t4 ln t leads to a multisheeted singularity structure of great complexity this structure is built recursively from an elemental pattern which takes the form of four armed stars of singularities this construction is deduced analytically from the properties of the mapping z t4 ln t and is confirmed quite accurately numerically a systematic resummation of the psi series in terms of lame functions is developed this series exhibits the same analytic structure at all orders and provides a semi local analytical representation of the solution which is apparently valid even in the chaotic regime

robust estimation of generalized linear models with measurement errors this paper considers consistent estimation of generalized linear models with covariate measurement errors in contrast to the previous approach of assuming that measurement errors are normally distributed we make no distributional assumptions on the latent variables or the measurement errors using the results of li j econometrics 110 2002 1 on the nonparametric identification and estimation of the distribution of the latent variables when replicate measurements are available we propose to maximize the criterion based on an asymptotically corrected likelihood we show that such an estimator is consistent we also evaluate the finite sample performance of our estimator through a monte carlo study

new similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations the author discusses similarity reductions and painleve analysis for the symmetric regularised long wave and modified benjamin bona mahoney equations 1972 both of which arise in several physical applications including shallow water waves both equations are thought to non integrable i e not solvable by inverse scattering since numerical studies show that the interaction of solitary waves in inelastic in particular we determine some new similarity reductions of the symmetric regularised long wave equation these new similarity reductions are not obtainable using the classical lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method which involves no group theoretical techniques it is shown that every similarity reduction of both the symmetric regularised long wave and modified benjamin bona mahoney equations obtained using the classical lie group method reduces the associated partial differential equation to an ordinary differential equation of painleve type whereas the new similarity solution of the symmetric regularised long wave equation reduces it to an ordinary differential equation which is not of painleve type it is also shown that neither the symmetric regularised long wave equation nor the modified benjamin bona mahoney equation possesses the painleve property for partial differential equations as defined by weiss et al 1983

a semiparametric joint model for longitudinal and survival data with application to hemodialysis study in many longitudinal clinical studies the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject s susceptibility to progression of the disease it is of scientific and clinical interest to relate such quantities to a later time to event clinical endpoint such as patient survival this is usually done with a shared parameter model in such models the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject level severity or susceptibility also called frailty in statistical terms in this article we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed effect model and the conditional distribution of the survival data is given by a cox proportional hazard model we allow unknown regression coefficients and time dependent covariates in both models the proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters an idea that originated from correction of covariate measurement error in measurement error models the corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators unlike most published methods for joint modeling the proposed estimation procedure does not rely on distributional assumptions of the frailties the proposed method was studied in simulations and applied to a data set from the hemodialysis study

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

the generalized damped cubic equation integrability and general solution the nonlinear ordinary differential equation of the form u f1u f2u f3u3 o representing a generalized damped cubic equation is fully analysed the author finds the general expression for f2 in terms of f1 and f3 that renders the equation integrable also he shows that if f2 satisfies the above mentioned condition the former nonlinear differential equation can always be reduced through adequate changes of variable to the second painleve transcendent

the analytic structure of dynamical systems and self similar natural boundaries abstract in this paper we investigate the analytic complex time structure of the movable singularities for several dynamical systems in general it is found that there exists a direct connection between the occurencce of a certain type of multiple valuedness of the singularities and the existence of a class of remarkable self similar natural boundaries for these systems an asymptotic description of the distribution of singularities in the natural boundary is developed this provides a description of the fine scale structure of these natural boundaries that agrees closely with the numerical calculations

using simex for smoothing parameter choice in errors in variables problems simex methods are attractive for solving curve estimation problems in errors in variables regression using parametric or semiparametric techniques however nonparametric approaches are generally of quite a different type being based on for example kernels local linear modeling ridging orthogonal series or splines all of these techniques involve the challenging and not well studied issue of empirical smoothing parameter choice we show that simex can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors in variable regression in particular we suggest an approach based on multiple error inflated or remeasured data sets and extrapolation

tests for detecting overdispersion in models with measurement error in covariates measurement error in covariates can affect the accuracy in count data modeling and analysis in overdispersion identification the true mean variance relationship can be obscured under the influence of measurement error in covariates in this paper we propose three tests for detecting overdispersion when covariates are measured with error a modified score test and two score tests based on the proposed approximate likelihood and quasi likelihood respectively the proposed approximate likelihood is derived under the classical measurement error model and the resulting approximate maximum likelihood estimator is shown to have superior efficiency simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi likelihood and other alternatives in terms of empirical power by analyzing a real dataset containing the health related quality of life measurements of a particular group of patients we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results copyright 2015 john wiley sons ltd

a regularization corrected score method for nonlinear regression models with covariate error present here a new general method for adjusting for covariate error our method consists of an approximate version of the stefanski nakamura corrected score approach using the method of regularization to obtain an approximate solution of the relevant integral equation we develop the theory in the setting of classical likelihood models this setting covers for example linear regression nonlinear regression logistic regression and poisson regression the method is extremely general in terms of the types of measurement error models covered and is a functional method in the sense of not involving assumptions on the distribution of the true covariate we discuss the theoretical properties of the method and present simulation results in the logistic regression setting univariate and multivariate for illustration we apply the method to data from the harvard nurses health study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer

on the singularity analysis of intersecting separatrices in near integrable dynamical systems abstract it has been recently proved by s l ziglin that transversal intersections of separatrices invariant manifolds in near integrable hamiltonian systems of two degrees of freedom imply the existence of multi valued solutions with infinitely many riemann sheets ziglin s theorem is illustrated here on a simple example and then extended and applied to non hamiltonian analytic flows x f x eg x t with x x y and g x t g x t 2 which for e 0 possess the painleve property on the other hand the theoretically expected logarithmic singularities for e 0 are obtained explicitly in solutions near the intersecting separatrices thus we conjecture that dynamical systems with the painleve property can have no separatrix intersections and hence no strange attractors etc these singularities are then numerically located and found to form certain very interesting chimney patterns in the complex t plane on which they accumulate densely the upper part of the chimneys away from the re t axis is asymptotically quite insensitive to changes in parameter values or initial conditions the singularity pattern itself however becomes denser and each chimney is seen to gradually collapse towards the re t axis as the amplitude of the driving term increases and the motion becomes more chaotic

semiparametric approaches for joint modeling of longitudinal and survival data with time varying coefficients we study joint modeling of survival and longitudinal data there are two regression models of interest the primary model is for survival outcomes which are assumed to follow a time varying coefficient proportional hazards model the second model is for longitudinal data which are assumed to follow a random effects model based on the trajectory of a subject s longitudinal data some covariates in the survival model are functions of the unobserved random effects estimated random effects are generally different from the unobserved random effects and hence this leads to covariate measurement error to deal with covariate measurement error we propose a local corrected score estimator and a local conditional score estimator both approaches are semiparametric methods in the sense that there is no distributional assumption needed for the underlying true covariates the estimators are shown to be consistent and asymptotically normal however simulation studies indicate that the conditional score estimator outperforms the corrected score estimator for finite samples especially in the case of relatively large measurement error the approaches are demonstrated by an application to data from an hiv clinical trial

prediction in the presence of measurement error general discussion and an example predicting defoliation motivated by the particular problem of predicting defoliation based on a measure of gypsy moth egg mass density prediction in the presence of measurement error is discussed the measurement error variances and covariances are allowed to vary from unit to unit and are estimated by some type of within unit sampling a general discussion is given as to when one should correct for the measurement error and a method of estimating the prediction standard deviation is given when a correction is needed the results are illustrated with the defoliation example

analytic structure of the henon heiles hamiltonian in integrable and nonintegrable regimes the solutions of the henon heiles hamiltonian are investigated in the complex time plane the use of the painleve property i e the property that the only movable singularities exhibited by the solution are poles enables successful prediction of the values of the nonlinear coupling parameter for which the system is integrable special attention is paid to the structure of the natural boundaries that are found in some of the nonintegrable regimes these boundaries have a remarkable self similar structure whose form changes as a function of the nonlinear coupling

integrating the nonintegrable analytic structure of the lorenz system revisited abstract a study of the complex time analytic structure of the lorenz system in nonintegrable parameter regimes reveals the special sets of parameter values for which one time dependent integral of motion exists furthermore the analysis yields the exact form of the part of the integral with the highest homogeneous weight and a method to construct the rest of the integral recursive clustering of singularities in the chaotic regimes of the system is observed in computer studies and explained by a simple analytic argument the analytic techniques used in these studies a systematic resummation of a logarithmic psi series appears to be quite general and can provide explicit representations of a solution even in the chaotic regimes in the neighborhood of a given movable singularity furthermore we suggest that this technique provides a type of renormalization program to study a wide class of nonintegrable systems

the singularity analysis for nearly integrable systems homoclinic intersections and local multivaluedness abstract in this study a new perturbative scheme for nonintegrable ordinary differential equations is proposed these perturbative expansions are based on the singularity analysis of the unperturbed system and is performed in the neighborhood of its singularities under suitable conditions on the homoclinic structure of the unperturbed system the melnikov vector can be computed based on the knowledge of the laurent expansions of the solutions the existence of transverse homoclinic intersections is therefore explicitly related to the existence of critical points for the solutions in the complex plane of the independent variable

varying coefficients model with measurement error we propose a semiparametric partially varying coefficient model to study the relationship between serum creatinine concentration and the glomerular filtration rate gfr among kidney donors and patients with chronic kidney disease a regression model is used to relate serum creatinine to gfr and demographic factors in which coefficient of gfr is expressed as a function of age to allow its effect to be age dependent gfr measurements obtained from the clearance of a radioactively labeled isotope are assumed to be a surrogate for the true gfr with the relationship between measured and true gfr expressed using an additive error model we use locally corrected score equations to estimate parameters and coefficient functions and propose an expected generalized cross validation egcv method to select the kernel bandwidth the performance of the proposed methods which avoid distributional assumptions on the true gfr and residuals is investigated by simulation accounting for measurement error using the proposed model reduced apparent inconsistencies in the relationship between serum creatinine and gfr among different clinical data sets derived from kidney donor and chronic kidney disease source populations

some effects of ignoring correlated measurement errors in straight line regression and prediction instructive expressions are developed for expected values of the least squares regression coefficient sample residual mean squared error and squared sample correlation coefficient in terms of a general measurement error model allowing for correlated measurement errors these expressions are useful in assessing the importance of measurement error in given applications and can be inverted to give simple estimators of measurement error model parameters based on the usual least squares estimates they show that in certain circumstances the correlation of variables contaminated with measurement errors can be greater than that of the uncontaminated variables these simple expressions should be useful in promoting the use of measurement error models in applications an example demonstrates that even in some cases where the least squares regression coefficient is affected little by measurement error valid estimation of the standard error of prediction may require the use of a measurement error model

boosting as a regularized path to a maximum margin classifier in this paper we study boosting methods from a new perspective we build on recent work by efron et al to show that boosting approximately and in some cases exactly minimizes its loss criterion with an l1 constraint on the coefficient vector this helps understand the success of boosting with early stopping as regularized fitting of the loss criterion for the two most commonly used criteria exponential and binomial log likelihood we further show that as the constraint is relaxed or equivalently as the boosting iterations proceed the solution converges in the separable case to an l1 optimal separating hyper plane we prove that this l1 optimal separating hyper plane has the property of maximizing the minimal l1 margin of the training data as defined in the boosting literature an interesting fundamental similarity between boosting and kernel support vector machines emerges as both can be described as methods for regularized optimization in high dimensional predictor space using a computational trick to make the calculation practical and converging to margin maximizing solutions while this statement describes svms exactly it applies to boosting only approximately

estimating a nonlinear function of a normal mean summary we derive a monte carlo amenable minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator applications to problems arising in the analysis of data measured with error are described

a modified estimating equation approach to correcting for measurement error in regression summary a modified estimating equation approach is proposed to correct for measurement error in regression problems we allow changing measurement error variances and covariances across units allow the regressors to be fixed allow estimation of the measurement error variances covariances and account for uncertainty arising from this estimation and explicitly model measurement error in the response multiple linear quadratic poisson and logistic regression are considered in detail and it is seen that some previously developed estimators arise as special cases from the proposed approach a small simulation study is presented for logistic regression

polynomial regression with errors in the variables a polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients assuming hypothetically the latent true regressor variable to be known and then adjusting for the errors if normality of the error variables can be assumed the estimator can be simplified considerably only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known if the variance of the errors in the dependent variable is also known another estimator can be constructed

corrected score estimation in the proportional hazards model with misclassified discrete covariates we consider cox proportional hazards regression when the covariate vector includes error prone discrete covariates along with error free covariates which may be discrete or continuous the misclassification in the discrete error prone covariates is allowed to be of any specified form building on the work of nakamura and his colleagues we present a corrected score method for this setting the method can handle all three major study designs internal validation design external validation design and replicate measures design both functional and structural error models and time dependent covariates satisfying a certain localized error condition we derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix we present the results of a finite sample simulation study under weibull survival with a single binary covariate having known misclassification rates the performance of the method described here was similar to that of related methods we have examined in previous works specifically our new estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study our method generally performed well in these simulations the new estimator has a broader range of applicability than many other estimators proposed in the literature including those described in our own earlier work in that it can handle time dependent covariates with an arbitrary misclassification structure we illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer

oscillatory finite time singularities in finance population and rupture abstract we present a simple two dimensional dynamical system where two nonlinear terms exerting respectively positive feedback and reversal compete to create a singularity in finite time decorated by accelerating oscillations the power law singularity results from the increasing growth rate the oscillations result from the restoring mechanism as a function of the order of the nonlinearity of the growth rate and of the restoring term a rich variety of behavior is documented analytically and numerically the dynamical behavior is traced back fundamentally to the self similar spiral structure of trajectories in phase space unfolding around an unstable spiral point at the origin the interplay between the restoring mechanism and the nonlinear growth rate leads to approximately log periodic oscillations with remarkable scaling properties three domains of applications are discussed 1 the stock market with a competition between nonlinear trend followers and nonlinear value investors 2 the world human population with a competition between a population dependent growth rate and a nonlinear dependence on a finite carrying capacity 3 the failure of a material subjected to a time varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing

polynomial regression and estimating functions in the presence of multiplicative measurement error we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor two general methods are considered with the methods differing in their assumptions about the distributions of the predictor and the measurement errors consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory diagnostics are presented for distinguishing additive and multiplicative measurement error data from a nutrition study are analysed by using the methods the results from a simulation study are presented and the performances of the methods are compared

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

invertible point transformations painleve analysis and anharmonic oscillators the techniques of an invertible point transformation and the painleve analysis can be used to construct integrable ordinary differential equations the authors compare both techniques for anharmonic oscillators

estimation of the quadratic errors in variables model summary an estimator is presented for the coefficients of the quadratic functional relationship the estimator is shown to be asymptotically normally distributed as the sample size increases in deriving this result it is not assumed that replication occurs a monte carlo study is presented agreeing well with the asymptotic results an example from the earth sciences is analysed

a pseudo partial likelihood method for semiparametric survival regression with covariate errors this article presents an estimator for the regression coefficient vector in the cox proportional hazards model with covariate error the estimator is obtained by maximizing a likelihood type function similar to the cox partial likelihood the likelihood function involves the cumulative baseline hazard function for which a simple estimator is substituted the method is capable of handling general covariate error structures it is not restricted to the independent additive error model it can be applied to studies with either an external or internal validation sample and also to studies with replicate measurements of the surrogate covariate the estimator is shown to be consistent and asymptotically normal and an estimate of the asymptotic covariance matrix is derived some extensions to general transformation survival models are indicated simulation studies are presented for a setup with a single error prone binary covariate and a setup with a single error prone normally distributed covariate these si

trouble with gegenbauer reconstruction for defeating gibbs phenomenon runge phenomenon in the diagonal limit of gegenbauer polynomial approximations to defeat gibbs phenomenon in fourier and chebyshev series gottlieb et al d gottlieb c w shu a solomonoff h vandeven on the gibbs phenomenon i recovering exponential accuracy from the fourier partial sum of a nonperiodic analytic function j comput appl math 43 1992 81 98 developed a gegenbauer reconstruction the partial sums of the fourier or other spectral series are reexpanded as a series of gegenbauer polynomials c n m x recovering spectral accuracy even in the presence of shock waves or other discontinuities to achieve a rate of convergence which is exponential in n however gegenbauer reconstruction requires increasing the order m of the polynomials linearly with the truncation n of the series m bn for some constant b 0 when the order m is fixed it is well known that the gegenbauer series converges as n everywhere on x 1 1 if f x the function being expanded is analytic on the interval but what happens in the diagonal limit in which m n tend to infinity simultaneously we show that singularities of f x off the real axis can destroy convergence of this diagonal approximation process in the sense that the error diverges for subintervals of x 1 1 gegenbauer reconstruction must therefore be constrained to use a sufficiently small ratio of order m to truncation n this off axis singularity constraint is likely to impair the effectiveness of the reconstruction in some applications

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

cox regression with accurate covariates unascertainable a nonparametric correction approach abstract many survival studies involve covariates that are not accurately ascertainable cd4 lymphocyte count in hiv aids research is a typical example for which the gold standard of the measurement is not available this article proposes a consistent estimation procedure for cox regression under the additive measurement error model distinct from existing methods the proposed estimation for regression coefficients does not require any additional assumptions we establish the normalized partial score function as a functional of empirical processes which facilitates the construction of an estimating function with the same limit using replicated mismeasured covariates the resulting regression coefficient estimators are shown to be consistent and asymptotically normal a consistent sandwich variance estimate is presented we also suggest estimators for the baseline cumulative hazard function numerical studies demonstrate that the procedure performs well under practical sample sizes application to an aid

asymptotic analysis of time singularities for a class of time dependent hamiltonians we analyse the local and global structure of time singularities for a class of quasi integrable hamiltonian systems in the arnold liouville sense we show that there is good agreement between the numerically observed local behaviour of the solutions and the perturbative scheme we produce using asymptotic approximations of the solution around the singularities we also prove the convergence of the psi series associated to the movable singularities of the systems considered we also propose a simple model in order to analyse the global structure of the singularities in the directions of exponential growth of the potential in time

corrected loss estimation for quantile regression with covariate measurement errors we study estimation in quantile regression when covariates are measured with errors existing methods require stringent assumptions such as spherically symmetric joint distribution of the regression and measurement error variables or linearity of all quantile functions which restrict model flexibility and complicate computation in this paper we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression the proposed method is simple to implement its validity requires only linearity of the particular quantile function of interest and it requires no parametric assumptions on the regression error distributions finite sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered

adjusting for covariate errors with nonparametric assessment of the true covariate distribution a well known and useful method for generalised regression analysis when a linear covariate x is available only through some approximation z is to carry out more or less the usual analysis with e x z substituted for x sometimes but not always the quantity var x z should be used to allow for overdispersion introduced by this substitution these quantities involve the distribution of true covariates x and with some exceptions this requires assessment of that distribution through the distribution of observed values z it is often desirable to take a nonparametric approach to this which inherently involves a deconvolution that is difficult to carry our directly however if covariate errors are assumed to be multiplicative and log normal simple but accurate approximations are available for the quantities e x k z k 1 2 in particular the approximations depend only on the first two derivatives of the logarithm of the density of z at the point under consideration and the coefficient of variation of z x the methods will thus be most useful in large scale observational studies where the distribution of z can be assessed well enough in an essentially nonparametric manner to approximate adequately those derivatives we consider both the classical and berkson error models this approach is applied to radiation dose estimates for atomic bomb survivors

corrected score estimation via complex variable simulation extrapolation a monte carlo method of computing unbiased estimating equations for the analysis of data measured with error is described asymptotic distribution results are obtained for estimators derived from the monte carlo estimating equations the method is illustrated with examples applications and simulation studies the monte carlo estimating equations are corrected scores in the sense of nakamura and the proposed methods are closely related to the simulation method described by cook and stefanski