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

an extended hazard model with longitudinal covariates summary in clinical trials and other medical studies it has become increasingly common to observe an event time of interest and longitudinal covariates simultaneously in the literature joint modelling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified survival model most commonly the cox proportional model in this paper we propose a general class of semi parametric hazard regres

a nonparametric estimation procedure for bivariate extreme value copulas summary a bivariate extreme value distribution with fixed marginals is generated by a onedimensional map called a dependence function this paper proposes a new nonparametric estimator of this function its asymptotic properties are examined and its small sample behaviour is compared to that of other rank based and likelihood based procedures the new estimator is shown to be uniformly strongly convergent and asymptotically unbiased through simulations it is also seen to perform reasonably well against the maximum likelihood estimator based on the correct model and to have smaller l1 l2 and l errors than any existing nonparametric alternative the n consistency of the proposed estimator leads to nonparametric estimation of tawn s 1988 dependence measure that may be used to test independence in small samples

an example of a gas system which can be destabilized by an integrable perturbation a construction of a globally asymptotically stable time invariant system which can be destabilized by some integrable perturbation is given besides its intrinsic interest this serves to provide counterexamples to an open question regarding lyapunov functions

derivation of the wave function collapse in the context of nelson s stochastic mechanics the von neumann collapse of the quantum mechanical wave function after a position measurement is derived by a purely probabilistic mechanism in the context of nelson s stochastic mechanics

on the φ0 stability of comparison differential systems for many years now the variety of problems of the qualitative properties of differential equations in the context of lyaponov second method has been successfully investigated in a unified way using the comparison principle s in this method the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comparison equations in order to successfully employ this method it is generally required that the comparison systems possess some special properties the conditions under which the scalar comparison equations possess positivity and stability behaviour have been investigated using scalar lyapunov function method by brauer l siljak and grujic 9 and others ladde 3 gave suficient conditions for nonnegativity and stability of solutions of systems of comparison equations in his investigation of stability of comparison differential systems ladde 3 considered the asymptotic stability and exponential asymptotic stability of the comparison differential system using the method of vector lyapunov functions however imbedded in the method of vector lyapunov function is the requirement of quasimonotone nondecreasing property of the comparison system but quasimonotonicity of the comparison system is not a necessary condition for the system to be stable thus the limitation of the application potential of this general and effective method is due to the fact that

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

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

maximum likelihood localization of sources in noise modeled as a stable process this paper introduces a new class of robust beamformers which perform optimally over a wide range of non gaussian additive noise environments the maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature the analysis is based on the assumption that the additive noise can be modeled as a complex symmetric spl alpha stable s spl alpha s process transform based approximations of the likelihood estimation are used for the general s spl alpha s class of distributions while the exact probability density function is used for the cauchy case it is shown that the cauchy beamformer greatly outperforms the gaussian beamformer in a wide variety of non gaussian noise environments and performs comparably to the gaussian beamformer when the additive noise is gaussian the cramer rao bound for the estimation error variance is derived for the cauchy case and the robustness of the s spl alpha s beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments

measurement error in linear autoregressive models time series data are often subject to measurement error usually the result of needing to estimate the variable of interest although it is often reasonable to assume that the measurement error is additive i e the estimator is conditionally unbiased for the missing true value the measurement error variances often vary as a result of changes in the population process over time and or changes in sampling effort in this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors allowing heteroscedasticity in the measurement error variances we establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the yule walker estimating equations we also examine a pseudo likelihood method based on normality assumptions and computed using the kalman filter we review other techniques that have been proposed including two that require no information about

marginal models for the analysis of longitudinal measurements with nonignorable non monotone missing data summary we propose methods for the analysis of continuous responses subject to nonignorable non monotone missing data we form a pseudolikelihood by naively assuming independence over time and using a product of marginal likelihoods at each time point and we obtain consistent and asymptotically normal estimators of the mean and missingness parameters our primary interest is in estimating the parameters of the marginal model at each time point and we make no assumption about the correlation structure an approximate variance is found for the parameter estimates using a sandwich estimate we provide an example and present a simulation study that assesses the performance of the model

semiparametric pseudo likelihoods in generalized linear models with nonignorable missing data we consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified we adopt a pseudo likelihood approach that makes use of an instrumental variable to help identifying unknown parameters in the presence of nonignorable missing data explicit conditions for the identifiability of parameters are given some asymptotic properties of the parameter estimators based on maximizing the pseudo likelihood are established explicit asymptotic covariance matrix and its estimator are also derived in some cases for the numerical maximization of the pseudo likelihood we develop a two step iteration algorithm that decomposes a nonconcave maximization problem into two problems of maximizing concave functions some simulation results and an application to a dataset from cotton factory workers are also presented

semiparametric approach to regression with a covariate subject to a detection limit we consider generalized linear regression with a covariate left censored at a lower detection limit complete case analysis where observations with values below the limit are eliminated yields valid estimates for regression coefficients but loses efficiency ad hoc substitution methods are biased and parametric maximum likelihood estimation relies on parametric models for the unobservable tail probability distribution and may suffer from model misspecification to obtain robust and more efficient results we propose a semiparametric likelihood based approach using an accelerated failure time model for the covariate subject to the detection limit a two stage estimation procedure is developed where the conditional distribution of this covariate given other variables is estimated prior to maximizing the likelihood function the proposed method outperforms complete case analysis and substitution methods in simulation studies technical conditions for desirable asymptotic properties are provided

a bivariate pseudolikelihood for incomplete longitudinal binary data with nonignorable nonmonotone missingness for analyzing longitudinal binary data with nonignorable and non monotone missing responses a full likelihood method is complicated algebraically and often requires intensive computation especially when there are many follow up times as an alternative a pseudo likelihood approach has been proposed in the literature under minimal parametric assumptions this formulation only requires specification of the marginal distributions of the responses and missing data mechanism and uses an independence working assumption however this estimator can be inefficient for estimating both time varying and time stationary effects under moderate to strong within subject associations among repeated responses in this article we propose an alternative estimator based on a bivariate pseudo likelihood and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo likelihood obtained under the assumption of independence we illustrate the method using longitudinal data on cd4 counts from two clinical trials of hiv infected patients

logistic regression with incompletely observed categorical covariates a comparison of three approaches summary a logistic regression analysis based on the complete cases neglects the information due to subjects with missing values in at least one but not in all covariates three different approaches allowing the use of this information are compared maximum likelihood estimation pseudo maximum likelihood estimation and probability imputation the first two yield consistent estimates of the regression coefficients and asymptotic normality allows the construction of asymptotically valid confidence intervals the only necessary assumption is that the probability for the occurrence of missing values does not depend on the true value of the hidden covariates whereas there may be a dependence on completely observed covariates and on the outcome variable their relative efficiency and the gain relative to a complete case analysis is investigated comparison with imputation methods shows that imputation of conditional probabilities can be regarded as a close approximation to the pseudo maximum likelihood estimation whereas imputation of unconditional probabilities is associated with serious bias

unified analysis of secondary traits in case control association studies it has been repeatedly shown that in case control association studies analysis of a secondary trait that ignores the original sampling scheme can produce highly biased risk estimates although a number of approaches have been proposed to properly analyze secondary traits most approaches fail to reproduce the marginal logistic model assumed for the original case control trait and or do not allow for interaction between secondary trait and genotype marker on primary disease risk in addition the flexible handling of covariates remains challenging we present a general retrospective likelihood framework to perform association testing for both binary and continuous secondary traits which respects marginal models and incorporates the interaction term we provide a computational algorithm based on a reparameterized approximate profile likelihood for obtaining the maximum likelihood ml estimate and its standard error for the genetic effect on secondary traits in the presence of covariates for completen

combined estimating equation approaches for semiparametric transformation models with length biased survival data summary survival data are subject to length biased sampling when the survival times are left truncated and the underlying truncation time random variable is uniformly distributed substantial efficiency gains can be achieved by incorporating the information about the truncation time distribution in the estimation procedure wang 1989 journal of the american statistical association 84 742 748 wang 1996 biometrika 83 343 354 under the semiparametric transformation models the maximum likelihood method is expected to be fully efficient yet it is difficult to implement because the full likelihood depends on the nonparametric component in a complicated way moreover its asymptotic properties have not been established in this article we extend the martingale estimating equation approach chen et al 2002 biometrika 89 659 668 kim et al 2013 journal of the american statistical association 108 217 227 and the pseudo partial likelihood approach severini and wong 1992 the annals of statistics 4 1768 1802 zucker 2005 journal of the american statistical association 100 1264 1277 for semiparametric transformation models with right censored data to handle left truncated and right censored data in the same spirit of the composite likelihood method huang and qin 2012 journal of the american statistical association 107 946 957 we further construct another set of unbiased estimating equations by exploiting the special probability structure of length biased sampling thus the number of estimating equations exceeds the number of parameters and efficiency gains can be achieved by solving a simple combination of these estimating equations the proposed methods are easy to implement as they do not require additional programming efforts moreover they are shown to be consistent and asymptotically normally distributed a data analysis of a dementia study illustrates the methods

finite size effects in separable recurrent neural networks we perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics away from saturation we find two types of finite size effects thermal fluctuations and disorder induced frozen corrections to the mean field laws the finite size effects are described by equations that correspond to a time dependent ornstein uhlenbeck process we show how the theory can be used to understand and quantify various finite size phenomena in recurrent neural networks with and without detailed balance

an augmented probit model for missing predictable covariates in quantal bioassay with small sample size summary quantal bioassay experiments relate the amount or potency of some compound for example poison antibody or drug to a binary outcome such as death or infection in animals for infectious diseases probit regression is commonly used for inference and a key measure of potency is given by the idp the amount that results in p of the animals being infected in some experiments a validation set may be used where both direct and proxy measures of the dose are available on a subset of animals with the proxy being available on all the proxy variable can be viewed as a messy reflection of the direct variable leading to an errors in variables problem we develop a model for the validation set and use a constrained seemingly unrelated regression sur model to obtain the distribution of the direct measure conditional on the proxy we use the conditional distribution to derive a pseudo likelihood based on probit regression and use the parametric bootstrap for statistical inference we re evaluate an old experiment in 21 monkeys where neutralizing antibodies nabs to hiv were measured using an old proxy assay in all monkeys and with a new direct assay in a validation set of 11 who had sufficient stored plasma using our methods we obtain an estimate of the id1 for the new assay an important target for hiv vaccine candidates in simulations we compare the pseudo likelihood estimates with regression calibration and a full joint likelihood approach

estimating functions in chaotic systems abstract berliner considered bayesian and likelihood based approaches for estimation and prediction in a chaotic system with measurement error this article proposes the use of estimating functions for this problem logistic and exponential maps are analyzed estimators are shown to be consistent and asymptotically normal small sample behavior is studied with simulations

convergence time and finite size effects in neural networks the time needed for convergence to a stable state starting from an initial state having macroscopic overlap with a stored state is studied numerically for networks up to n 105 neurons although such systems are much larger than those traditionally used in studying neural networks they are still too small to extract reliable information about the asymptotic behaviour of the convergence time

hamilton s principle in stochastic mechanics in this paper we establish three variational principles that provide new foundations for nelson s stochastic mechanics in the case of nonrelativistic particles without spin the resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature we first develop two stochastic variational principles whose hamilton jacobi like equations are precisely the two coupled partial differential equations that are obtained from the schrodinger equation madelung equations the two problems are zero sum noncooperative stochastic differential games that are familiar in the control theory literature they are solved here by means of a new absolutely elementary method based on lagrange functionals for both games the saddle point equilibrium solution is given by the nelson s process and the optimal controls for the two competing players are precisely nelson s current velocity v and osmotic velocity u respectively the first variational principle includes as special cases both the guerra morato variational principle phys rev d 27 1774 1983 and schrodinger original variational derivation of the time independent equation it also reduces to the classical least action principle when the intensity of the underlying noise tends to zero it appears as a saddle point action principle in the second variational principle the action is simply the difference between the initial and final configurational entropy it is therefore a saddle point entropy production principle from the variational principles it follows in particular that both v x t and u x t are gradients of appropriate principal functions in the variational principles the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second combining the two variational principles we get the quantum hamilton principle i e a variational characterization of the logarithm of the wave function the lagrangian is the lagrangian of classical mechanics with the complex valued velocity v iu replacing the classical velocity the dynamics is given by a stochastic differential equation for real valued diffusions with complex valued drift and driving noise processes from the variational principle we derive a newton type law we finally define the momentum process and show that its mean and variance coincide with those of the quantum momentum operator

expected estimating equations to accommodate covariate measurement error estimating equations which are not necessarily likelihood based score equations are becoming increasingly popular for estimating regression model parameters this paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects but surrogate or mismeasured covariates are available instead the method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data we propose to base estimation on the expectation of the complete data estimating equation conditioned on available data the regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations the expected estimating equation eee estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data a pseudo eee estimator which requires less computation is also investigated asymptotic distribution theory is derived small sample simulations are conducted when the error process is an order 1 autoregressive model regression calibration is extended to this setting and compared with the eee approach we demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity

determining the value of additional surrogate exposure data for improving the estimate of an odds ratio we consider the design of both cohort and case control studies in which an initial stage 1 sample of complete data on an error free disease indicator d a correct gold standard dichotomous exposure measurement x and an error prone exposure measurement z are available we calculate the amount of additional information on the odds ratio relating d to x that one can obtain from a second stage 2 sample of measurements only on d and z if one allows for differential measurement error in z there is often little advantage in having more than four times as much data in stage 2 data as in stage 1 with the assumption that a non differential measurement error model is reasonable larger amounts of stage 2 data can be useful simulations indicate that stage 1 samples of modest size 50 cases in case control studies and 50 failures in cohort studies yield sufficiently reliable estimates of needed parameters to assist in determining an appropriate size for the stage 2 sample these ideas apply in settings either where the amount of stage 1 data is limited and fixed by external constraints or where one has gathered stage 1 data in advance to avoid collecting superfluous stage 2 data

inference in semiparametric regression models under partial questionnaire design and nonmonotone missing data in epidemiologic studies partial questionnaire design pqd can reduce cost time and other practical burdens associated with lengthy questionnaires by assigning different subsets of the questionnaire to different but overlapping subsets of the study participants in this article we describe methods for semiparametric inference for regression model under pqd and other study settings that can generate nonmonotone missing data in covariates in particular motivated from methods for multiphase designs we develop three estimators namely mean score pseudo likelihood and semiparametric maximum likelihood each of which has some unique advantages we develop the asymptotic theory and a sandwich variance estimator for each of the estimators under the underlying semiparametric model that allows the distribution of the covariates to remain nonparametric we study the finite sample performances and relative efficiencies of the methods using simulation studies we illustrate the methods using data from a ca

inference for the proportional hazards model with misclassified discrete valued covariates summary we consider the cox proportional hazards model with discrete valued covariates subject to misclassification we present a simple estimator of the regression parameter vector for this model the estimator is based on a weighted least squares analysis of weighted averaged transformed kaplan meier curves for the different possible configurations of the observed covariate vector optimal weighting of the transformed kaplan meier curves is described the method is designed for the case in which the misclassification rates are known or are estimated from an external validation study a hybrid estimator for situations with an internal validation study is also described when there is no misclassification the regression coefficient vector is small in magnitude and the censoring distribution does not depend on the covariates our estimator has the same asymptotic covariance matrix as the cox partial likelihood estimator we present results of a finite sample simulation study under weibull survival in the setting of a single binary covariate with known misclassification rates in this simulation study our estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we illustrate the method on data from a study of the relationship between trans unsaturated dietary fat consumption and cardiovascular disease incidence

uncertainty relations in stochastic mechanics position momentum uncertainty in nelson s stochastic mechanics phys rev 150 1079 1966 has previously been investigated by de la pena auerbach and cetto phys lett a 39 65 1972 in this paper their result is generalized and full equivalence between the uncertainty relations in stochastic mechanics and conventional quantum mechanics is established force momentum uncertainty is also considered

a copula model for repeated measurements with non ignorable non monotone missing outcome a normal copula based selection model is proposed for continuous longitudinal data with a non ignorable non monotone missing data process the normal copula is used to combine the distribution of the outcome of interest and that of the missing data indicators given the covariates parameters in the model are estimated by a pseudo likelihood method we first use the gee with a logistic link to estimate the parameters associated with the marginal distribution of the missing data indicator given the covariates assuming that covariates are always observed then we estimate other parameters by inserting the estimates from the first step into the full likelihood function a simulation study is conducted to assess the robustness of the assumed model under different missing data processes the proposed method is then applied to one example from a community cohort study to demonstrate its capability to reduce bias

lipschitz stability of nonlinear systems of differential equations in s the authors introduced the notion of lipschitz stability in differential equations this notion lies somewhere between uniform stability on one side and the notions of asymptotic stability in variation 3 and uniform stability in variation 4 on the other side however lipschitz stability is new only as a nonliner phenomenon since it coincides with uniform stability in linear systems s an important feature of lipschitz stability is that unlike uniform stability the linearized system inherits the property of lipschitz stability from the original nonlinear system 5 in this paper we pursue the study of lipschitz stability that started in s using essentially the techniques of liapunov functions then we give sufficient conditions for the lipschitz stability of certain nonlinearly pertur bed nonlinear systems such systems include among other equations certain integrodifferential and functional differential equations then we give an example which can be investigated successfully using our results but cannot be handled by any previous techniques or results 9

modeling functional data with spatially heterogeneous shape characteristics summary we propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location we use copulas so that the marginal distributions and the dependence structure can be modeled independently dependence is modeled with a gaussian or t copula so that there is an underlying latent gaussian process we model the marginal distributions using the skew t family the mean variance and shape parameters are modeled nonparametrically as functions of location a computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy tailed marginal distributions is introduced this framework provides a new set of tools for increasingly complex data collected in medical and public health studies our methods were motivated by and are illustrated with a state of the art study of neuronal tracts in multiple sclerosis patients and healthy controls using the tools we have developed we were able to find those locations along the tract most affected by the disease however our methods are general and highly relevant to many functional data sets in addition to the application to one dimensional tract profiles illustrated here higher dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging mri

estimating the number of classes estimating the unknown number of classes in a population has numerous important applications in a poisson mixture model the problem is reduced to estimating the odds that a class is undetected in a sample the discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one sided confidence intervals for the number of classes are also necessarily one sided a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes

analysis of multivariate missing data with nonignorable nonresponse we consider multivariate regression analysis with missing data in the outcome variables when the nonresponse mechanism depends on the underlying values of the responses and hence is nonignorable related problems include response biased sampling where data are sampled with probability depending only on the univariate response our methods do not require specification of the form of the nonresponse mechanism we show that under certain regularity conditions all the regression parameters can be identified from a conditional likelihood based on the complete cases if the marginal distribution of the covariates is known if the marginal distribution of the covariates is estimated from the data then the regression parameters are identified from a pseudolikelihood resulting from substituting the estimated marginal distribution of the covariates in the above conditional likelihood simulation studies suggest that the pseudolikelihood method is approximately unbiased in order to identify the model parameters usually the dimension of the covariates and observed responses is required to be at least as large as the dimension of the missing responses the method can also be modified to handle partial information about the missing data mechanism we also consider the special case where the missing data have a monotone pattern where better use of the incomplete information can be made under certain assumptions

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

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

efficient regression calibration for logistic regression in main study internal validation study designs with an imperfect reference instrument an extension to the version of the regression calibration estimator proposed by rosner et al for logistic and other generalized linear regression models is given for main study internal validation study designs this estimator combines the information about the parameter of interest contained in the internal validation study with rosner et al s regression calibration estimate using a generalized inverse variance weighted average it is shown that the validation study selection model can be ignored as long as this model is jointly independent of the outcome and the incompletely observed covariates conditional at most upon the surrogates and other completely observed covariates in an extensive simulation study designed to follow a complex multivariate setting in nutritional epidemiology it is shown that with validation study sizes of 340 or more this estimator appears to be asymptotically optimal in the sense that it is nearly unbiased and nearly as efficient as a properly specified maximum likelihood estimator a modification to the regression calibration variance estimator which replaces the standard uncorrected logistic regression coefficient variance with the sandwich estimator to account for the possible misspecification of the logistic regression fit to the surrogate covariates in the main study was also studied in this same simulation experiment in this study the alternative variance formula yielded results virtually identical to the original formula a version of the proposed estimator is also derived for the case where the reference instrument available only in the validation study is imperfect but unbiased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument replicate measures are obtained in a subset of study participants in this case it is shown that the validation study selection model can be ignored when sampling into the validation study depends at most only upon perfectly measured covariates two data sets a study of fever in relation to occupational exposure to antineoplastics among hospital pharmacists and a study of breast cancer incidence in relation to dietary intakes of alcohol and vitamin a adjusted for total energy intake from the nurses health study were analysed using these new methods in these data because the validation studies contained less than 200 observations and the events of interest were relatively rare as is typical the potential improvements offered by this new estimator were not apparent

efficient analysis of case control studies with sample weights analysis of population based case control studies with complex sampling designs is challenging because the sample selection probabilities and therefore the sample weights depend on the response variable and covariates commonly the design consistent weighted estimators of the parameters of the population regression model are obtained by solving sample weighted estimating equations weighted estimators however are known to be inefficient when the weights are highly variable as is typical for case control designs in this paper we propose two alternative estimators that have higher efficiency and smaller finite sample bias compared with the weighted estimator both methods incorporate the information included in the sample weights by modeling the sample expectation of the weights conditional on design variables we discuss benefits and limitations of each of the two proposed estimators emphasizing efficiency and robustness we compare the finite sample properties of the two new estimators and traditionally used weighted estimators with the use of simulated data under various sampling scenarios we apply the methods to the u s kidney cancer case control study to identify risk factors published 2012 this article is a us government work and is in the public domain in the usa

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

stochastic mechanics and the feynman integral the feynman integral is given a stochastic interpretation in the framework of nelson s stochastic mechanics employing a time symmetric variant of nelson s kinematics recently developed by the author

fully parametric and semi parametric regression models for common events with covariate measurement error in main study validation study designs the derivation of the likelihood function for binary data from two types of main study validation study designs where model covariates are measured with error is elaborated rather than limiting consideration to a restricted family of models with convenient mathematical properties we suggest that empirical considerations customized to the data at hand should drive model choices the joint likelihood function for the main study in which the covariates are measured with error and the validation study in which they are not is maximized and estimation and inference proceeds using standard theory although the choice of the measurement error model is driven by empirical considerations the relatively small validation study sizes typically seen may lead to misspecification resulting in bias in estimation and inference about exposure disease relationships by using a nonparametric form for the measurement error model the resulting semi parametric methods suggested by robins rotnitzky and zhao 1994 journal of the american statistical association 89 864 866 and robins hsieh and newey 1995 journal of the royal statistical society series b 57 409 424 are free from bias due to misspecification of the measurement error model trading efficiency for robustness as usual these fully and semi parametric methods are illustrated with a detailed example from a main study validation study of the health effects of occupational exposure to chemotherapeutics among pharmacists valanis et al 1993 american journal of hospital pharmacy 50 455 462 a constant prevalence ratio model for common binary events with gamma covariate measurement error is derived and empirically verified by the available data a careful reanalysis of the data taking measurement error fully into account leads to a threefold increase in the log relative risk and no loss of statistical power the semi parametric estimates are consistent with the parametric results providing reassurance that important bias due to misspecification of the measurement error model is unlikely

on the asymptotic behaviour of the pseudolikelihood ratio test statistic with boundary problems this paper considers the asymptotic distribution of the likelihood ratio statistic t for testing a subset of parameter of interest h 0 0 based on the pseudolikelihood l where is a consistent estimator of the nuisance parameter we show that the asymptotic distribution of t under h 0 is a weighted sum of independent chi squared variables some sufficient conditions are provided for the limiting distribution to be a chi squared variable when the true value of the parameter of interest 0 or the true value of the nuisance parameter 0 lies on the boundary of parameter space the problem is shown to be asymptotically equivalent to the problem of testing the restricted mean of a multivariate normal distribution based on one observation from a multivariate normal distribution with misspecified covariance matrix or from a mixture of multivariate normal distributions a variety of examples are provided for which the limiting distributions of t may be mixtures of chi squared variables we conducted simulation studies to examine the performance of the likelihood ratio test statistics in variance component models and teratological experiments

statistical inference based on pseudo maximum likelihood estimators in elliptical populations in this article we develop statistical inference based on the maximum likelihood method in elliptical populations with an unknown density function the method assuming the multivariate normal distribution using the sample mean and the sample covariance matrix is basically correct even for elliptical populations under a certain kurtosis adjustment but is not statistically efficient especially when the kurtosis of the population distribution has higher than moderate values on the other hand several methods of statistical inference assuming a particular family e g multivariate t distribution of elliptical distributions have been recommended as a robust procedure against outliers or distributions with heavy tails such inference also will be important to maintain a high efficiency of statistical inference in elliptical populations in practice however it is very difficult to choose an appropriate family of elliptical distributions and one may misspecify the family furthermore extra parameters

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 composite likelihood approach to latent multivariate gaussian modeling of snp data with application to genetic association testing many statistical tests have been proposed for case control data to detect disease association with multiple single nucleotide polymorphisms snps in linkage disequilibrium the main reason for the existence of so many tests is that each test aims to detect one or two aspects of many possible distributional differences between cases and controls largely due to the lack of a general and yet simple model for discrete genotype data here we propose a latent variable model to represent snp data the observed snp data are assumed to be obtained by discretizing a latent multivariate gaussian variate because the latent variate is multivariate gaussian its distribution is completely characterized by its mean vector and covariance matrix in contrast to much more complex forms of a general distribution for discrete multivariate snp data we propose a composite likelihood approach for parameter estimation a direct application of this latent variable model is to association testing with multiple snps in a candidate gene or region in contrast to many existing tests that aim to detect only one or two aspects of many possible distributional differences of discrete snp data we can exclusively focus on testing the mean and covariance parameters of the latent gaussian distributions for cases and controls our simulation results demonstrate potential power gains of the proposed approach over some existing methods

analysing bivariate survival data with interval sampling and application to cancer epidemiology in biomedical studies ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease in cancer studies interest could be focused on bivariate failure times for example time from birth to cancer onset and time from cancer onset to death this paper considers a sampling scheme termed interval sampling in which the first failure event is identified within a calendar time interval the time of the initiating event can be retrospectively confirmed and the occurrence of the second failure event is observed subject to right censoring in a cancer data application the initiating first and second events could correspond to birth cancer onset and death the fact that the data are collected conditional on the first failure event occurring within a time interval induces bias interval sampling is widely used for collection of disease registry data by governments and medical institutions though the interval sampling bias is frequently overlooked by researchers this paper develops statistical methods for analysing such data semiparametric methods are proposed under semi stationarity and stationarity numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes we apply the proposed methods to ovarian cancer registry data

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

perturbing families of lyapunov functions and stability in terms of two measures on considere les proprietes de stabilite non uniforme en termes de deux mesures en employant des familles perturbantes de fonctions de lyapunov

regression analysis with censored autocorrelated data abstract for many studies in which data are collected sequentially in time the sensitivity of the measurement is limited and an exact value can be recorded only if it falls within a specified range this gives rise to a censored time series in this article we present a methodology for regression analysis of censored time series data we fit autoregressive models to account for the time dependence two numerical methods for full likelihood estimation and an approximate method are discussed the methods are illustrated with air pollution data subject to lower limits of detection

brief solving optimal control problems by means of general lagrange functionals the method of lagrange functionals is applied to the optimal control of systems with quadratic and implicit dynamics

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

modelling marginal hazards in multivariate failure time data we consider the problem of estimating relative risk parameters in the marginal distribution of failure times from a sample in which individuals are grouped into clusters and failure times for individuals within clusters may be dependent we assume that the marginal hazard of failure for individuals within a cluster is specified by a relative risk regression model and the structure of dependence between individuals within a cluster is left unspecified estimating equations for the regression parameters and an estimator for the cumulative base line marginal hazard are described

a maximum pseudo profile likelihood estimator for the cox model under length biased sampling this paper considers semiparametric estimation of the cox proportional hazards model for right censored and length biased data arising from prevalent sampling to exploit the special structure of length biased sampling we propose a maximum pseudo profile likelihood estimator which can handle time dependent covariates and is consistent under covariate dependent censoring simulation studies show that the proposed estimator is more efficient than its competitors a data analysis illustrates the methods and theory

random systems described with stochastic velocities abstract kinematics of stochastic mechanics is used to study diffusion problems at a more general level without forcing a link to newtonian mechanics stochastic velocities are taken from nelson s kinematics to study nonlinear random systems random effects are systematically separated from the deterministic motion via a transformation to fluctuation variables then closed expressions for stochastic velocities are written and as a consequence analytical applications can be developed a system is studied to show the difference between detailed and nondetailed balance besides a one dimensional problem is considered to characterize the relaxation process the concept of entropy is introduced to find an expression describing stationary processes so that one has two kind of tools to study this type of problems the final result is that a few simple techniques are put together to describe a wide amount of phenomena

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

empirical likelihood in missing data problems missing data is a ubiquitous problem in medical and social sciences it is well known that inferences based only on the complete data may not only lose efficiency but may also lead to biased results if the data is not missing completely at random mcar the inverse probability weighting method proposed by horvitz and thompson 1952 is a popular alternative when the data is not mcar the horvitz thompson method however is sensitive to the inverse weights and may suffer from loss of efficiency in this paper we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters one important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations the proposed method can achieve semiparametric efficiency if the probabilit

capacity of networks with correlated attractors we analyse the extensive loading of the neural network model proposed to describe neurophysiological experiments in which correlated attractors associated to uncorrelated patterns are found the phase diagram is obtained and discussed some generalizations of the original model are also considered in all the cases we demonstrate the existence of a region in the phase diagram with correlated attractors results from numerical simulations which confirm the mean field theory results are also presented

pseudo maximum likelihood estimation the asymptotic distribution gong and samaniego 1981 define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates this note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate

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

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

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

logistic regression for two stage case control data summary samples of diseased cases and nondiseased controls are drawn at random from the population at risk after classification according to the exposure of interest subsamples of cases and controls are selected for purposes of covariable ascertainment a modification of the usual logistic regression analysis yields consistent estimates of covariable adjusted relative risks and their standard errors by balancing the numbers of exposed and nonexposed for whom covariable inforniation is ascertained within case and control samples some efficiency may be gained over the usual single stage design particularly when the exposure is rare and the relative risks associated with the covariables are large the procedure may be useful also when covariable information is missing for a large part of the sample

macroscopic lyapunov functions for separable stochastic neural networks with detailed balance we derive macroscopic lyapunov functions for large long range ising spin neural networks with separable symmetric interactions which evolve in time according to local field alignment we generalize existing constructions which correspond todeterministic zero temperature evolution and to specific choices of the interaction structure to the case ofstochastic evolution and arbitrary separable interaction matrices for both parallel and sequential spin updating we find a direct relation between the form of the lyapunov functions which describe dynamical processes and the saddle point integration that results from performing equilibrium statistical mechanical studies of the present type of model

modeling clustered discrete or grouped time survival data with covariates summary we have developed methods for modeling discrete or grouped time right censored survival data collected from correlated groups or clusters we assume that the marginal hazard of failure for individual items within a cluster is specified by a linear log odds survival model and the dependence structure is based on a gamma frailty model the dependence can be modeled as a function of cluster level covariates likelihood equations for estimating the model parameters are provided generalized estimating equations for the marginal hazard regression parameters and pseudolikelihood methods for estimating the dependence parameters are also described data from two clinical trials are used for illustration purposes

1 dimensional attractor neural networks we solve a class of attractor neural network models with a mixture of 1d nearest neighbour interactions and infinite range interactions which are both of a hebbian type form our solution is based on a combination of mean field methods transfer matrices and 1d random field techniques and is obtained both for boltzmann type equilibrium following sequential glauber dynamics and peretto type equilibrium following parallel dynamics competition between the alignment forces mediated via short range interactions and those mediated via infinite range ones is found to generate novel phenomena such as multiple locally stable pure states first order transitions between recall states 2 cycles and non recall states and domain formation leading to extremely long relaxation times we test our results against numerical simulations and simple benchmark cases and find excellent agreement

lagrange lemma and the optimal control of diffusions ii nonlinear lagrange functionals abstract in kosmol 1991 kosmol and pavon 1993 a new elementary approach to optimal control problems relying on the lagrange lemma was described which appears to be technically and conceptually much simpler than existing methods and furthermore provides a unified variational approach in kosmol and pavon 1992 this method was further clarified and developed for linear lagrange functionals we devote this second paper to nonlinear lagrange functionals the power of this approach is here clearly demonstrated in particular it is shown that the nonlinear lagrange functional induced by the value function of the problem is just one of the many functionals which may effectively be employed to solve control problems see examples 1 and 2 in section 3 moreover in our approach we can deal in the same framework with problems with state constraints or nonsmooth problems hence the lagrange functionals approach provides new tools to solve control problems which may be readily applied even when existing approaches fail

extremal flows in wasserstein space we develop an intrinsic geometric approach to the calculus of variations in the wasserstein space we show that the flows associated with the schrodinger bridge with general prior with optimal mass transport and with the madelung fluid can all be characterized as annihilating the first variation of a suitable action we then discuss the implications of this unified framework for stochastic mechanics it entails in particular a sort of fluid dynamic reconciliation between bohm s and nelson s stochastic mechanics we develop an intrinsic geometric approach to the calculus of variations in the wasserstein space we show that the flows associated with the schrodinger bridge with general prior with optimal mass transport and with the madelung fluid can all be characterized as annihilating the first variation of a suitable action we then discuss the implications of this unified framework for stochastic mechanics it entails in particular a sort of fluid dynamic reconciliation between bohm s and nelson s stochastic mechanics

on stability of nonlinear systems of ordinary differential equations the notions of f 0 stability h 0 h stability integral and eventual stability of nonlinear systems of ordinary differential equations ode s are introduced our aim in this paper is to improve and extend these notions to new types of stability namely f 0 l p stability h 0 h integral stability and h 0 h eventual stability of systems of ode s respectively and given some criteria our technique depends on liapunov direct method