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

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

nonlinear and nonparametric regression and instrumental variables we consider regression when the predictor is measured with error and an instrumental variable iv is available the regression function can be modeled linearly nonlinearly or nonparametrically our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions much weaker than previously known to imply identifiability in addition we exploit a characterization of the iv estimator as a classical correction for attenuation method based on a particular estimate of the variance of the measurement error this estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution the functional estimators uses simulation extrapolation or deconvolution kernels and the structural method uses bayesian markov chain monte carlo

nonparametric regression in the presence of measurement error summary in many regression applications the independent variable is measured with error when this happens conventional parametric and nonparametric regression techniques are no longer valid we consider two diverent approaches to nonparametric regression the first uses the simex simulation extrapolation method and makes no assumption about the distribution of the unobserved error prone predictor for this approach we derive an asymptotic theory for kernel regression which has some surprising implications penalised regression splines are also considered for fixed number of known knots the second approach assumes that the error prone predictor has a distribution of a mixture of normals with an unknown number of components and uses regression splines simulations illustrate the results

measurement error modelling with an approximate instrumental variable summary consider using regression modelling to relate an exposure predictor variable to a disease outcome response variable if the exposure variable is measured with error but this error is ignored in the analysis then misleading inferences can result this problem is well known and has spawned a large literature on methods which adjust for measurement error in predictor variables one theme is that the requisite assumptions about the nature of the measurement error can be stronger than what is actually known in many practical situations in particular the assumptions that are required to yield a model which is formally identified from the observable data can be quite strong the paper deals with one particular strategy for measurement error modelling namely that of seeking an instrumental variable i e a covariate s which is associated with exposure and conditionally independent of the outcome given exposure if these two conditions hold exactly then we call s an exact instrumental variable and an identified model results however the second is not checkable empirically since the actual exposure is unobserved in practice then investigators typically seek a covariate which is plausibly thought to satisfy it we study inferences which acknowledge the approximate nature of this assumption in particular we consider bayesian inference with a prior distribution that posits that s is probably close to conditionally independent of outcome given exposure we refer to this as an approximate instrumental variable assumption although the approximate instrumental variable assumption is more realistic for most applications concern arises that a non identified model may result thus the paper contrasts inferences arising from the approximate instrumental variable assumption with their exact instrumental variable counterparts with particular emphasis on the benefit of basing inferences on a more realistic model versus the cost of basing inferences on a non identified model

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

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

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

estimation for polynomial structural equation models abstract structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing subject matter needs for considering nonlinear structural models have been well documented but current fitting procedures are available only for a limited class of models in this article a systematic statistical approach is developed for the general polynomial structural equation model the new procedure applies a method of moments procedure similar to the one used in errors in variables regression to the factor score estimates from the measurement model fit the asymptotic properties of the estimator are derived and a modified estimator with better small sample properties is introduced simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods an example from a substance abuse prevention study is also discussed

monte carlo methods for nonparametric regression with heteroscedastic measurement error nonparametric regression is a fundamental problem in statistics but challenging when the independent variable is measured with error among the first approaches was an extension of deconvoluting kernel density estimators for homescedastic measurement error the main contribution of this article is to propose a new simulation based nonparametric regression estimator for the heteroscedastic measurement error case similar to some earlier proposals our estimator is built on principles underlying deconvoluting kernel density estimators however the proposed estimation procedure uses monte carlo methods for estimating nonlinear functions of a normal mean which is different than any previous estimator we show that the estimator has desirable operating characteristics in both large and small samples and apply the method to a study of benzene exposure in chinese factory workers

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

generalized varying coefficient models for longitudinal data summary we propose a generalization of the varying coefficient model for longitudinal data to cases where not only current but also recent past values of the predictor process affect current response more precisely the targeted regression coefficient functions of the proposed model have sliding window supports around current time t a variant of a recently proposed two step estimation method for varying coefficient models is proposed for estimation in the context of these gener alized varying coefficient models and is found to lead to improvements especially for the case of additive measurement errors in both response and predictors the proposed methodology for estimation and inference is also applicable for the case of additive measurement error in the com mon versions of varying coefficient models that relate only current observations of predictor and response processes to each other asymptotic distributions of the proposed estimators are derived and the model is applied to the problem of predicting protein concentrations in a longitudinal study simulation studies demonstrate the efficacy of the proposed estimation procedure

a class of asymptotically efficient noniterative estimators of a common odds ratio summary a new class of noniterative estimators of a common odds ratio is presented it is shown that the principle of construction leads to asymptotically optimal estimators that is estimators which are consistent asymptotically normally distributed and asymptotically efficient

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

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

some aspects of measurement error in explanatory variables for continuous and binary regression models a simple form of measurement error model for explanatory variables is studied incorporating classical and berkson cases as particular forms and allowing for either additive or multiplicative errors the work is motivated by epidemiological problems and therefore consideration is given not only to continuous response variables but also to logistic regression models the possibility that different individuals in a study have errors of different types is also considered the relatively simple estimation procedures proposed for use with cohort data and case control data are checked by simulation under the assumption of various error structures the results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values the work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure but it should be applicable to a wide variety of situations

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

empirical bias bandwidths for local polynomial nonparametric regression and density estimation abstract a data based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials the estimator called the empirical bias bandwidth selector ebbs is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function ebbs minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term the variance term used is exact not asymptotic though it involves the conditional variance of the response given the predictors that must be estimated the bias term is estimated empirically not from an asymptotic expression thus ebbs is similar to the double smoothing approach of hardle hall and marron and a local bandwidth selector of schucany but is developed here for a far wider class of estimation problems than what those authors considered ebbs is tested on simulated data and its performance seems quite satisfactory local polynomial smoothing of a histogram is a high

proportional hazards model with covariate measurement error and instrumental variables in biomedical studies covariates with measurement error may occur in survival data existing approaches mostly require certain replications on the error contaminated covariates which may not be available in the data in this article we develop a simple nonparametric correction approach for estimation of the regression parameters in the proportional hazards model using a subset of the sample where instrumental variables are observed the instrumental variables are related to the covariates through a general nonparametric model and no distributional assumptions are placed on the error and the underlying true covariates we further propose a novel generalized methods of moments nonparametric correction estimator to improve the efficiency over the simple correction approach the efficiency gain can be substantial when the calibration subsample is small compared to the whole sample the estimators are shown to be consistent and asymptotically normal performance of the estimators is evaluated via simulatio

residual based diagnostics for structural equation models classical diagnostics for structural equation models are based on aggregate forms of the data and are ill suited for checking distributional or linearity assumptions we extend recently developed goodness of fit tests for correlated data based on subject specific residuals to structural equation models with latent variables the proposed tests lend themselves to graphical displays and are designed to detect misspecified distributional or linearity assumptions to complement graphical displays test statistics are defined the null distributions of the test statistics are approximated using computationally efficient simulation techniques the properties of the proposed tests are examined via simulation studies we illustrate the methods using data from a study of in utero lead exposure

locally efficient estimators for semiparametric models with measurement error we derive constructive locally efficient estimators in semiparametric measurement error models the setting is one in which the likelihood function depends on variables measured with and without error where the variables measured without error can be modeled nonparametrically the algorithm is based on backfitting we show that if one adopts a parametric model for the latent variable measured with error and if this model is correct then the estimator is semiparametric efficient if the latent variable model is misspecified then our methods lead to a consistent and asymptotically normal estimator our method further produces an estimator of the nonparametric function that achieves the standard bias and variance property we extend the methodology to allow estimation of parameters in the measurement error model by additional data in the form of replicates or instrumental variables the methods are illustrated through a simulation study and a data example where the putative latent variable distribution i

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

silhouette based gait recognition using procrustes shape analysis and elliptic fourier descriptors this paper presents a gait recognition method which combines spatio temporal motion characteristics statistical and physical parameters referred to as stm spp of a human subject for its classification by analysing shape of the subject s silhouette contours using procrustes shape analysis psa and elliptic fourier descriptors efds stm spp uses spatio temporal gait characteristics and physical parameters of human body to resolve similar dissimilarity scores between probe and gallery sequences obtained by psa a part based shape analysis using efds is also introduced to achieve robustness against carrying conditions the classification results by psa and efds are combined resolving tie in ranking using contour matching based on hu moments experimental results show stm spp outperforms several silhouette based gait recognition methods

matching shape sequences in video with applications in human movement analysis we present an approach for comparing two sequences of deforming shapes using both parametric models and nonparametric methods in our approach kendall s definition of shape is used for feature extraction since the shape feature rests on a non euclidean manifold we propose parametric models like the autoregressive model and autoregressive moving average model on the tangent space and demonstrate the ability of these models to capture the nature of shape deformations using experiments on gait based human recognition the nonparametric model is based on dynamic time warping we suggest a modification of the dynamic time warping algorithm to include the nature of the non euclidean space in which the shape deformations take place we also show the efficacy of this algorithm by its application to gait based human recognition we exploit the shape deformations of a person s silhouette as a discriminating feature and provide recognition results using the nonparametric model our analysis leads to some interesting observations on the role of shape and kinematics in automated gait based person authentication

finite sample properties of some old and some new estimators of a common odds ratio from multiple 2 2 tables abstract a simulation study was used to determine the finite sample properties of various estimators of a common odds ratio from multiple 2 2 tables the maximum likelihood mantel haenszel and woolf estimators plus four variants of each were considered the original woolf estimator and one of its variants are dismissed on the grounds that they often cannot be calculated in terms of minimum bias maximum likelihood is the recommended procedure after adding 25 to each cell

simulation extrapolation the measurement error jackknife abstract this article provides theoretical support for our simulation based estimation procedure simex for measurement error models we do so by establishing a strong relationship between simex estimation and jackknife estimation a result of our investigation is the identification of a variance estimation method for simex that parallels jackknife variance estimation data from the framingham heart study are used to illustrate the variance estimation procedure in logistic regression measurement error models

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

the consistency of posterior distributions in nonparametric problems we give conditions that guarantee that the posterior probability of every hellinger neighborhood of the true distribution tends to 1 almost surely the conditions are 1 a requirement that the prior not put high mass near distributions with very rough densities and 2 a requirement that the prior put positive mass in kullback leibler neighborhoods of the true distribution the results are based on the idea of approximating the set of distributions with a finite dimensional set of distributions with sufficiently small hellinger bracketing metric entropy we apply the results to some examples

simulation extrapolation estimation in parametric measurement error models we describe a simulation based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated the method entails adding add

a jackknife estimator of a combined odds ratio a jackknife estimator of a common odds ratio is derived in the situation of stratified contingency tables it is based on pseudovalues that are constructed by omitting each single observation in each cell by means of monte carlo experiments this estimator is compared with the estimators of woolf mantel and haenszel and another jackknife estimator by breslow and liang of the common odds ratio in the situations considered this estimator has lower bias and mean squared error than the other three proposals the accompanying jackknife variance behaves in general similarly to the estimated variances of the woolf estimator and the mantel haenszel estimator

recognizing gaits across views through correlated motion co clustering human gait is an important biometric feature which can be used to identify a person remotely however view change can cause significant difficulties for gait recognition because it will alter available visual features for matching substantially moreover it is observed that different parts of gait will be affected differently by view change by exploring relations between two gaits from two different views it is also observed that a part of gait in one view is more related to a typical part than any other parts of gait in another view a new method proposed in this paper considers such variance of correlations between gaits across views that is not explicitly analyzed in the other existing methods in our method a novel motion co clustering is carried out to partition the most related parts of gaits from different views into the same group in this way relationships between gaits from different views will be more precisely described based on multiple groups of the motion co clustering instead of a single correlation descriptor inside each group a linear correlation between gait information across views is further maximized through canonical correlation analysis cca consequently gait information in one view can be projected onto another view through a linear approximation under the trained cca subspaces in the end a similarity between gaits originally recorded from different views can be measured under the approximately same view comprehensive experiments based on widely adopted gait databases have shown that our method outperforms the state of the art

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

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

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

silhouette analysis based gait recognition for human identification human identification at a distance has recently gained growing interest from computer vision researchers gait recognition aims essentially to address this problem by identifying people based on the way they walk in this paper a simple but efficient gait recognition algorithm using spatial temporal silhouette analysis is proposed for each image sequence a background subtraction algorithm and a simple correspondence procedure are first used to segment and track the moving silhouettes of a walking figure then eigenspace transformation based on principal component analysis pca is applied to time varying distance signals derived from a sequence of silhouette images to reduce the dimensionality of the input feature space supervised pattern classification techniques are finally performed in the lower dimensional eigenspace for recognition this method implicitly captures the structural and transitional characteristics of gait extensive experimental results on outdoor image sequences demonstrate that the proposed algorithm has an encouraging recognition performance with relatively low computational cost

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

mpca multilinear principal component analysis of tensor objects this paper introduces a multilinear principal component analysis mpca framework for tensor object feature extraction objects of interest in many computer vision and pattern recognition applications such as 2d 3d images and video sequences are naturally described as tensors or multilinear arrays the proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation the solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems as part of this work methods for subspace dimensionality determination are proposed and analyzed it is shown that the mpca framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis pca and its 2d variant 2d pca finally a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy and applied to the problem of gait recognition results presented here indicate mpca s utility as a feature extraction tool it is shown that even without a fully optimized design an mpca based gait recognition module achieves highly competitive performance and compares favorably to the state of the art gait recognizers