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

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

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

online calibration via variable length computerized adaptive testing item calibration is an essential issue in modern item response theory based psychological or educational testing due to the popularity of computerized adaptive testing methods to efficiently calibrate new items have become more important than that in the time when paper and pencil test administration is the norm there are many calibration processes being proposed and discussed from both theoretical and practical perspectives among them the online calibration may be one of the most cost effective processes in this paper under a variable length computerized adaptive testing scenario we integrate the methods of adaptive design sequential estimation and measurement error models to solve online item calibration problems the proposed sequential estimate of item parameters is shown to be strongly consistent and asymptotically normally distributed with a prechosen accuracy numerical results show that the proposed method is very promising in terms of both estimation accuracy and efficiency the results of using calibrated items to estimate the latent trait levels are also reported

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

score tests in generalized linear measurement error models summary hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x the efficient score test for the hypothesis of no association depends on the conditional expectation e xi w which is generally unknown the usual test substitutes w for e xi w and is asymptotically valid but not efficient we investigate two new test statistics appropriate when w x z where z is an independent measurement error the first is a wald test based on estimators corrected for measurement error despite the correction for attenuation in the estimator this test has the same local power as the usual test the second test employs an estimator of e x i w and is both asymptotically efficient for normal errors and approximately efficient when the measurement error variance is small

proportional hazards model with covariates subject to measurement error when covariates of a proportional hazards model are subject to measurement error the maximum likelihood estimates of regression coefficients based on the partial likelihood are asymptotically biased prentice 1982 biometrika 69 331 342 presents an example of such bias and suggests a modified partial likelihood this paper applies the corrected score function method nakamura 1990 biometrika 77 127 137 to the proportional hazards model when measurement errors are additive and normally distributed the result allows a simple correction to the ordinary partial likelihood that yields asymptotically unbiased estimates the validity of the correction is confirmed via a limited simulation study

representation complexity of adaptive 3d distance fields in this paper we study the representation complexity of a kind of data structure that stores the information necessary to compute the distance from a point to a geometric body these data structures called adaptive splitting based on cubature distance fields asbcdf are binary search trees generated by the adaptive splitting based on cubature asbc algorithm that adaptively subdivides the space surrounding the body into tetrahedra their representation complexity is measured by the number of nodes in the tree two times the number of tetrahedra in the resulting tessellation in the case of convex polyhedra we prove that this quantity remains bounded as the number of vertices of the polyhedra increases to infinity experimental results show that the number of tetrahedra in the tessellations is almost independent of the combinatorial complexity of the polyhedra this means that the average compute time of the distance to arbitrary convex polyhedra is almost constant therefore asbcdfs are especially suitable for real time applications involving rapidly changing environments modelized with complex polyhedra

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

slope estimation in the presence of informative right censoring modeling the number of observations as a geometric random variable summary a method is proposed for the estimation of rate of change from incomplete longitudinal data where the number of observations made for each subject is assumed to vary depending on the level of the response variable the proposed method involves a random slope model in which the number of observations is modeled as a geometric distribution with its mean dependent on the individual subject s rate of change the method adjusts for informative right censoring and provides estimates of the slopes of individual subjects as well as of the population under noninformative right censoring these estimators of the slopes are equivalent to bayes estimators fearn 1975 biometrika 62 89 100 the simulation study demonstrates that in cases where the censoring process is informative the proposed estimator is more efficient than either the unweighted or weighted estimator of slope the method is illustrated by the analysis of renal transplant data

semiparametric quasilikelihood and variance function estimation in measurement error models abstract we consider a quasilikelihood variance function model when a predictor x is measured with error and a surrogate w is observed when in addition to a primary data set containing y w a validation data set exists for which x w is observed we can i estimate the first and second moments of the response y given w by kernel regression ii use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters the estimators are shown to be asymptotically normally distributed with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates a more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n 1 3

the effect of measurement error summary measurement error causes the distribution generating data to differ from the distribution that is of substantive interest to understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error this paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error these provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present and the basis for the development of tests to detect measurement error and of models which incorporate its influence

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

instrumental variable estimation in binary regression measurement error models abstract we describe two approaches to instrumental variable estimation in binary regression measurement error models the methods entail constructing approximate mean models for the binary response as a function of the measured predictor the instrument and any covariates in the model estimates are obtained by exploiting relationships between regression parameters just as in linear instrumental variable estimation in the course of deriving the approximate mean models we obtain an alternative characterization of instrumental variable estimation in linear measurement error models

a bayesian approach to logistic regression models having measurement error following a mixture distribution to estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error we take a bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value we allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure we apply the method to study the risk of alcohol consumption on breast cancer using the nurses health study data we estimate measurement error from a small subsample where we compare true with reported consumption some of the self reported non drinkers truly do not drink the resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error

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

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

two stage instrumental variables estimators for the nonlinear errors in variables model abstract estimation for the nonlinear functional errors in variables model is considered under the assumption that instrumental variables are available the approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived utilizing the nonlinearity of the relationship an estimator of the error covariance matrix is introduced using the error covariance matrix estimator two types of two stage instrumental variable estimators are proposed the two two stage estimators do not have the asymptotic bias due to the nonlinearity a monte carlo experiment also shows the superiority of the two stage estimators over the ordinary estimator

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

estimation and inference for logistic regression with covariate misclassification and measurement error in main study validation study designs abstract in epidemiological studies continuous covariates often are measured with error and categorical covariates often are misclassified using the logistic regression model to represent the relationship between the binary outcome and the perfectly measured and classified covariates the model for the observed main study data is derived this derivation relies on the assumption that the error in the continuous covariates is multivariate normally distributed and uses a chain of logistic regression models to describe the misclassification processes these model assumptions are empirically verified in the validation study where the misclassified and mismeasured covariates are validated using perfectly measured and classified data the full data likelihood including contributions from both the main study and the validation study is maximized to obtain the maximum likelihood estimates for the parameters of the underlying logistic regression model and of the measurement error model and reclassification mo

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

cost efficient study designs for binary response data with gaussian covariate measurement error summary when mismeasurement of the exposure variable is anticipated epidemiologic cohort studies may be augmented to include a validation study where a small sample of data relating the imperfect exposure measurement method to the better method is collected optimal study designs i e least expensive subject to specified power constraints are developed that give the overall sample size and proportion of the overall sample size allocated to the validation study if better exposure measurements can be collected on a sample of subjects an optimal design can be suggested that conforms to realistic budgetary constraints the properties of three designs those that include an internal validation study those where the validated subsample is derived from subjects external to the primary investigation and those that use the better method of exposure assessment on all subjects are compared the proportion of overall study resources allocated to the validation substudy increases with increasing sample disease frequency decreasing unit cost of the superior exposure measurement relative to the imperfect one increasing unit cost of outcome ascertainment increasing distance between two alternative values of the relative risk between which the study is designed to discriminate and increasing magnitude of hypothesized values this proportion also depends in a nonlinear fashion on the severity of measurement error and when the validation study is internal measurement error reaches a point after which the optimal design is the smaller fully validated one

a new online calibration method for multidimensional computerized adaptive testing multidimensional method a m method a has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing mcat chen xin paper presented at the 78th meeting of the psychometric society arnhem the netherlands 2013 however a key assumption of m method a is that it treats person parameter estimates as their true values thus this method might yield erroneous item calibration when person parameter estimates contain non ignorable measurement errors to improve the performance of m method a this paper proposes a new mcat online calibration method namely the full functional mle m method a ffmle m method a this new method combines the full functional mle jones jin in psychometrika 59 59 75 1994 stefanski carroll in annals of statistics 13 1335 1351 1985 with the original m method a in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration two correction schemes are also proposed when implementing the new method a simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original m method a in almost all conditions

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

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

coupling integral and geometrical representations for vibro acoustical problems the finite element method is limited either to small geometries or to the low frequency range whereas geometrical approaches are best applied at medium and high frequencies but do not take vibrating surfaces into account when the vibrating boundaries of a volume are only a small part of the total boundary it is worth combining the two methods by using geometrical methods to compute a green function that includes all wave reflections on the surfaces of the volume it is possible to restrict the integral representation of the pressure field to the vibrating surfaces the surfaces to be meshed will be reduced to surfaces with known velocity fields this approach offers a means of reducing computation times it has been applied to large volumes corresponding to a room with a vibrating concrete wall and to a train with a vibrating window

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 comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

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

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

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

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