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

structural optimal control for safe petri nets this article addresses the problem of forbidden states in both conservative and non conservative safe petri net pn models the property of conservativeness is discussed and its implications are analysed the construction and formulation of control conditions in the context of safe and non conservative pn models is investigated emphasising the problem of control optimality the fundamental issue studied is that of the equivalence between a forbidden state and its associated constraint a new fashion of writing control conditions is proposed and used in conjunction with the place invariant synthesis method for the generation of a control solution the final controlled model obtained is a pn similar in size to the initial model finally the approach is illustrated via a simple example

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

optimal transform formed by a combination of nonlinear operators the case of data dimensionality reduction in this paper a new approach to constructing optimal nonlinear transforms of random vectors is proposed and justified the proposed transform t sub p is presented in the form of a sum with p terms where each term is interpreted as a particular rank reduced transform moreover terms in t sub p are represented as a combination of three operations f sub k q sub k and spl psi sub k with k 1 p the prime idea is to determine f sub k separately for each k 1 p from an associated rank constrained minimization problem similar to that used in the karhunen loe spl grave ve transform klt the operations q sub k and spl psi sub k are auxiliary for finding f sub k the contribution of each term in t sub p improves the entire transform performance a rigorous analysis of errors associated with the proposed transforms is given it is shown that the proposed transform improves such characteristics of rank reduced transforms as compression ratio and the accuracy of decompression and reduces required computational work the fourier series in hilbert space the wiener filter the klt and the transforms presented in earlier author papers in the field are particular cases of the proposed method theoretical results are illustrated with numerical simulations

some aspects of measurement error in a censored regression model abstract when a linear model with a censored dependent variable is written as a regression model the model is nonlinear in the explanatory variables this means that when the explanatory variables are measured with error estimation by instrumental variables will not lead to consistent estimates of the parameters my approach to the problem involves assuming that the variables measured with error can be represented by a reduced form equation and estimating the parameters of the censored regression model by the least absolute deviations estimator this estimator is based on the median of the distribution of the dependent variable rather than the mean and the median is not affected by censoring in the lower tail hence the estimator is consistent under general conditions i also consider the problem of testing for the presence of measurement error

the limiting distribution of least squares in an errors in variables regression model abstract there is a substantial literature concerning linear regression when some of the predictors independent variables are measured with error such models are of importance in econometrics instrumental variables models psychometrics correction for attenuation models of change and in instrumental calibration studies in medicine and industry recent theoretical work concerning maximum likelihood estimation in such models appears in healy 1980 fuller 1980 and anderson 1984 while reilly and patino leal 1981 take a bayesian approach in an applied context an investigator may either overlook the measurement errors in the predictors or choose the classical ordinary least squares ols estimator of the parameters because of its familiarity and ease of use certainly the methodology of classical least squares theory confidence intervals multiple comparisons tests of hypotheses residual analysis is considerably more developed than the corresponding errors in variables methodology particularly in samples of moderate size in this paper it is shown that under reasonable regularity conditions such linear combinations are jointly asymptotically normally distributed

estimating a covariance matrix from incomplete realizations of a random vector it is desired to estimate the mean and the covariance matrix of a gaussian random vector from a set of independent realizations with the complication that not every component of each realization of the random vector is observed subject to some restrictions the authors obtained an exact noniterative solution for the maximum likelihood ml estimates of the mean and the covariance matrix the ml estimate of the covariance matrix that is obtained from the set of incomplete realizations is guaranteed to be positive definite in contrast to ad hoc approaches based on averaging products of components from the same realization the key to obtaining the ml estimates is a tractable expression for the likelihood function in terms of the cholesky factors of the inverse covariance matrix with this formulation the ml estimates are found by fitting regression operators to appropriate subsets of the data the cholesky formulation also leads to a simple calculation by cramer rao bounds

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

algebraic connections between the least squares and total least squares problems in this paper the closeness of the total least squares tls and the classical least squares ls problem is studied algebraically interesting algebraic connections between their solutions their residuals their corrections applied to data fitting and their approximate subspaces are proven all these relationships point out the parameters which mainly determine the equivalences and differences between the two techniques these parameters also lead to a better understanding of the differences in sensitivity between both approaches with respect to perturbations of the data in particular it is shown how the differences between both approaches increase when the equationsax b become less compatible when the length ofb orx is growing or whena tends to be rank deficient they are maximal whenb is parallel with the singular vector ofa associated with its smallest singular value furthermore it is shown how tls leads to a weighted ls problem and assumptions about the underlying perturbation model of both techniques are deduced it is shown that many perturbation models correspond with the same tls solution

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

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

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

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

a bayesian study of the error in variables model this article presents the results of a study of the functional case of the problem of parameter estimation when there is error in all the variables there is consequently no distinction between independent and dependent variables posterior probability density functions are developed for the parameters with both linear and nonlinear and possibly multiple relations among the true values of the variables there is no distinction between models that are linear or nonlinear in the parameters the results are equivalent to generalizations of the work of some previous authors but lead to new and efficient algorithms for finding point estimates and their precisions for most of the results the error covariance matrix is assumed known though a case is treated where it is known except for a scalar multiplier the results are also shown to be valid if the covariance matrix is singular geometric interpretations are described

global identification of risk preferences with revealed preference data abstract the concept of parameter identification for a given specification is differentiated from global identification which specification is right first order conditions for production under risk are shown to admit many alternative specification pairs representing risk preferences and either perceived price risk production risk or the deterministic production structure imposing an arbitrary specification on any of the latter three determines which risk preference specification fits a given dataset undermining global identification even when parameter identification is suggested by typical statistics this lack of identification is not relaxed by increasing the number of observations critical implications for estimation of mean variance specifications are derived

estimators of odds ratio regression parameters in matched case control studies with covariate measurement error abstract this article studies estimators of the odds ratio and odds ratio regression parameters in finely matched case control studies containing a binary exposure of primary interest and subject specific covariates that are subject to measurement error a retrospective logistic regression model for the binary exposure variable is used the effect of measurement errors on the conditional maximum likelihood estimator is determined three alternatives are considered bias corrected functional and transformation estimators the asymptotic and small sample properties of the three competitors are studied the results are illustrated using data from a case control study of diet and colon cancer

estimation for the nonlinear functional relationship on etudie les proprietes asymptotiques de l estimateur du maximum de vraisemblance pour le modele fonctionnel implicite

instrumental variable estimation in generalized linear measurement error models abstract instrumental variable estimation in generalized linear measurement error models are studied for models with canonical link functions unbiased estimating equations are derived the maximum likelihood estimator for the normal theory structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein logistic regression is studied in detail an example is given and a simulation study described for the logistic model based on the framingham heart study data

control of vector discrete event systems ii controller synthesis this paper shows that associated control synthesis problems of ramadge wonham type can be efficiently solved under mild technical restrictions using elementary methods combined with linear integer programming both memoryless and dynamic state feedback are treated structural conditions are provided under which the controller can be computed in closed form namely represented as a vdes or generalized vdes gvdes the results are applied to a model of an agv system adapted from work of holloway and krogh 1990

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

data aided and non data aided maximum likelihood snr estimators for cpm data aided da and non data aided nda maximum likelihood ml estimators for the snr of cpm in the presence of phase and frequency offset are derived and analyzed cramer rao bounds for both are obtained and compared to the simulated performance of these estimators for a full response example cpsfk and a partial response example gmsk analysis and simulations show that the performance of the da ml estimator suffers from an unremovable bias caused by uncompensated frequency offset due to frequency offset estimation errors as a consequence the estimator error variance of the da ml estimator is not able to achieve its lower bound in contrast the estimator error variance of the nda ml estimator is capable of achieving its lower bound although the lower bound for nda ml estimator is higher than the lower bound for the da ml estimator this is because the nda ml estimator is not burdened with the requirement of relying on estimates of nuisance parameters the nda estimator only achieves its lower bound when the observation length or true snr are sufficiently large

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

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

infrastructure and productivity a nonlinear approach abstract this paper incorporates infrastructure into the production function as part of the technological constraint rather than as a discretionary factor input our theoretical model specifies a technological growth rate as a nonlinear function of infrastructure and a time trend the latter capturing the effect of all other variables on the growth rate in technology the time trend and infrastructure are modeled so as to be interactive rather than additive the functional form estimated allows for a s shaped production function which embodies not only the properties of a long run production function but also those exhibited in the short run

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

method of moments estimation and identifiability of semiparametric nonlinear errors in variables models abstract this paper deals with a nonlinear errors in variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric using the instrumental variable approach we propose method of moments estimators for the unknown parameters and simulation based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions moreover root n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and fourier deconvolution

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

the statistical behaviour of some least squares estimators of the centre and radius of a circle this paper examines the statistical behaviour of some least squares estimators of the centre and radius of a circle two error models are used the asymptotic consistency of the estimators is investigated where asymptotic consistency is established asymptotic covariance matrices are obtained a small sample simulation study gives results showing the same pattern as those of the asymptotic theory

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

instrumental variable estimator for the nonlinear errors in variables model abstract estimation for the nonlinear errors in variables model is considered it isassumed that additional information is available in the form of observations on instrumental variables an estimation procedure is presented for the parameters of the model asymptotic properties of the estimator are investigated

optimal exact designs on a circle or a circular arc fitting a circle to a set of data points on a plane is very common in engineering and science an important practical problem is how to choose the locations of measurement on a circular feature so far little attention has been paid to this design issue and only some simulation results are available in this paper for berman s bivariate four parameter model optimality is defined and shown to be equivalent to all p criteria with p 1 then optimal exact designs on a circle or a circular arc are derived for any sample size and sampling range as a by product 4 optimal approximate designs are also obtained these optimal designs are used to evaluate the efficiency of the equidistant sampling method widely used in practice these results also provide guidelines for users on sampling method and sample size selection

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

measuring information loss due to inconsistencies in duration data from longitudinal surveys abstract in this paper we take a functional errors in variables approach to modeling longitudinal duration data containing observed inconsistencies this approach separates the problem into two parts an errors in variables problem and an estimation problem this approach also enables us to develop measures of the effect of the data inconsistencies on the parameter estimates from a duration model one measure is the loss in precision in the parameter estimates that results from the inconsistencies we refer to the proportion of parameter variances that is due to the inconsistencies in the data as information loss the second is a distance measure which is used to provide information about how close we are to a consistent estimator an example is provided using a four month panel of current population survey data

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 class of semiparametric tests of treatment effect robust to confounder measurement error when assessing the presence of an exposure causal effect on a given outcome measurement error of a confounder can inflate the type i error rate of a treatment effect in even the simplest of settings in this paper we develop a large class of semiparametric test statistics of an exposure causal effect which are completely robust to additive unbiased measurement error of a subset of confounders a unique and appealing feature of our proposed methodology is that it requires no external information such as validation data or replicates of error prone confounders we present a doubly robust form of this test that requires the exposure mean model to be linear in the mismeasured confounders and only one of two models involving error free confounders to be correctly specified for the resulting test statistic to have correct type i error rate we demonstrate validity within our class of test statistics through simulation studies we apply the methods to a multi us city time series data set to test for an effect of temperature on mortality while adjusting for atmospheric particulate matter with diameter of 2 5 micrometres or less which is known to be measured with error

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

measurement error model collinearities collinearities can occur among the error free true predictors in measurement error models just as they occur among predictors in traditional regression models the coefficient estimators for measurement error models suffer the same ill effects of collinearities as do least squares estimators for linear measurement error models collinearities are a property of the secondorder moment matrix of the unobservable error free predictors for nonlinear models they are a property of the second order moment matrix of derivatives of the nonlinear function in this article collinearities among the predictors in measurement error models are defined and diagnostics for their detection are discussed the collinearity diagnostics introduced are similar to those used in traditional regression models but they are applied to estimated second order moment matrices of the error free predictors rather than to the second order moment matrix of the observed predictors examples are discussed one of which demonstrates th

on the use of compensated total least squares in system identification a bias compensated total least squares estimator is proposed for models which are linear in the parameters and nonlinear in the perturbed input and output signals the estimates are obtained using a noniterative and numerically stable method strong consistency of both the generalized total least squares and the compensated total least squares estimates are proven the theoretical properties are verified through simulations

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

comparison of least squares and errors in variables regression with special reference to randomized analysis of covariance abstract in an errors in variables regression model the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter we explore the conjecture that when the least squares estimate is consistent for a linear combination of the regression parameter it will be preferred to an errors in variables estimate at least asymptotically the conjecture is false in general but it is true for some important classes of problems one such problem is a randomized two group analysis of covariance upon which we focus

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

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

a simple estimator for nonlinear error in variable models we propose a simple estimator for nonlinear method of moment models with measurement error of the classical type when no additional data such as validation data or double measurements are available we assume that the marginal distributions of the measurement errors are laplace double exponential with zero means and unknown variances and the measurement errors are independent of the latent variables and are independent of each other under these assumptions we derive simple revised moment conditions in terms of the observed variables they are used to make inference about the model parameters and the variance of the measurement error the results of this paper show that the distributional assumption on the measurement errors can be used to point identify the parameters of interest our estimator is a parametric method of moments estimator that uses the revised moment conditions and hence is simple to compute our estimation method is particularly useful in situations where no additional data are available which is the case in many economic data sets simulation study demonstrates good finite sample properties of our proposed estimator we also examine the performance of the estimator in the case where the error distribution is misspecified

reduction of constraints for controller synthesis based on safe petri nets in this paper we present an efficient method based on safe petri nets to construct a controller a set of linear constraints allows forbidding the reachability of specific states the number of these so called forbidden states and consequently the number of constraints are large and lead to a large number of control places a systematic method to reduce the size and the number of constraints for safe petri nets is offered by using a method based on petri net invariants maximal permissive controllers are determined

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

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

robust and consistent estimation of nonlinear errors in variables models this paper considers the consistent estimation of nonlinear errors in variables models it adopts the functional modeling approach by assuming that the true but unobserved regressors are random variables but making no parametric assumption on the distribution from which the latent variables are drawn this paper shows how the information extracted from the replicate measurements can be used to identify and consistently estimate a general nonlinear errors in variables model the identification is established through characteristic functions the estimation procedure involves nonparametric estimation of the conditional density of the latent variables given the measurements using the identification results at the first stage and at the second stage a semiparametric nonlinear least squares estimator is proposed the consistency of the proposed estimator is also established finite sample performance of the estimator is investigated through a monte carlo study

estimation of structured covariance matrices and multiple window spectrum analysis a close relationship between low rank modeling and multiple window spectrum estimation is demonstrated by using maximum likelihood estimates of structured covariance matrices the power in a narrow spectral band is estimated by estimating the variances in a low rank signal plus noise covariance model this model is swept through the entire frequency band to obtain an estimate of power as a function of frequency the resulting spectrum estimates are given by weighted combinations of eigenspectra each eigenspectrum results from projecting the data onto an orthogonal component of the signal subspace and squaring the multiple window spectrum estimates of thomson 1982 correspond to a particular choice for the low rank signal model the low rank modeling and structured covariance matrix framework is also used to derive the maximum likelihood estimate for the center frequency of a signal in noise this estimate is also obtained from a weighted combination of eigenspectra

a general instrumental variable framework for regression analysis with outcome missing not at random summary the instrumental variable iv design is a well known approach for unbiased evaluation of causal effects in the presence of unobserved confounding in this article we study the iv approach to account for selection bias in regression analysis with outcome missing not at random in such a setting a valid iv is a variable which i predicts the nonresponse process and ii is independent of the outcome in the underlying population we show that under the additional assumption iii that the iv is independent of the magnitude of selection bias due to nonresponse the population regression in view is nonparametrically identified for point estimation under i iii we propose a simple complete case analysis which modifies the regression of primary interest by carefully incorporating the iv to account for selection bias the approach is developed for the identity log and logit link functions for inferences about the marginal mean of a binary outcome assuming i and ii only we describe novel and approximately sharp bounds which unlike robins manski bounds are smooth in model parameters therefore allowing for a straightforward approach to account for uncertainty due to sampling variability these bounds provide a more honest account of uncertainty and allows one to assess the extent to which a violation of the key identifying condition iii might affect inferences for illustration the methods are used to account for selection bias induced by hiv testing nonparticipation in the evaluation of hiv prevalence in the zambian demographic and health surveys

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

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

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

estimation for the box cox transformation model without assuming parametric error distribution box and cox proposed a power transformation for the response variable that yields a linear regression model with normal error and constant variance inference procedures for the regression coefficients and transformation parameter under this model setting have been studied extensively in this article we propose a simple semiparametric estimation method for the box cox transformation model with no specific parametric assumption on the distribution of the error term the resulting estimators are strongly consistent and asymptotically normal their covariance matrix can be estimated through a novel resampling method without involving nonparametric function estimates of the underlying unknown density function for the error term the new proposal is illustrated with a well known dataset in the literature of transformation and its efficiency and robustness are closely examined through numerical studies

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

estimation of nonlinear models with measurement error this paper presents a solution to an important econometric problem namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables when one repeated observation of each mismeasured regressor is available while a root n consistent estimator has been derived for polynomial specifications see hausman ichimura newey and powell 1991 such an estimator for general nonlinear specifications has so far not been available using the additional information provided by the repeated observation the suggested estimator separates the measurement error from the true value of the regressors thanks to a useful property of the fourier transform the fourier transform converts the integral equations that relate the distribution of the unobserved true variables to the observed variables measured with error into algebraic equations the solution to these equations yields enough information to identify arbitrary moments of the true unobserved variables the value of these moments can then be used to construct any estimator that can be written in terms of moments including traditional linear and nonlinear least squares estimators or general extremum estimators the proposed estimator is shown to admit a representation in terms of an influence function thus establishing its root n consistency and asymptotic normality monte carlo evidence and an application to engel curve estimation illustrate the usefulness of this new approach

a computational examination of orthogonal distance regression abstract ordinary least squares ols is one of the most commonly used criteria for fitting data to models and for estimating parameters orthogonal distance regression odr extends least squares data fitting to problems with independent variables that are not known exactly in this paper we present the results of an empirical study designed to compare ols to odr for fitting both linear and non linear models when there are errors in the independent variables the results indicate that for the data and performance criteria considered odr never performs appreciably worse than ols and often performs considerably better

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

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

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

brief identification of nonlinear errors in variables models a new identification algorithm for nonlinear but linear in parameters errors in variables models is presented using nonlinear polynomial eigenvalue eigenvector decompositions

a score test on measurement errors in rating transition times abstract we model credit rating histories as continuous time discrete state markov processes infrequent monitoring of the debtors solvency will result in erroneous observations of the rating transition times and consequently in biased parameter estimates we develop a score test against such measurement errors in the transition data that is independent of the error distribution we derive the asymptotic 2 distribution for the test statistic under the null by stochastic limit theory the test is applied to an international corporate portfolio while accounting for economic and debtor specific covariates the test indicates that measurement errors in the transition times are a real problem in practice