asymptotic properties of the maximum likelihood estimator in dichotomous logit models abstract the existence and strong consistency of the maximum likelihood estimator are analyzed in the context of dichotomous logit models sufficient conditions are given for the asymptotic normality of this estimator

paths on polymatroids this paper establishes bounds on the length of certain strictly monotone paths relative to a given linear objective function on a polymatroid or on the base of a polymatroid specialized bounds are given for a strict polymatroid and for a matroid polyhedron bounds on the diameter are included

modelling multivariate binary data with alternating logistic regressions marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables and the association between pairs of responses when the former is the scientific focus a first order generalized estimating equation method liang zeger 1986 is easy to implement and gives efficient estimates of regression coefficients although estimates of the association among the binary outcomes can be inefficient when the association model is a focus simultaneous modelling of the responses and all pairwise products prentice 1988 using second order estimating equations gives more efficient estimates of association parameters as well however this procedure can become computationally infeasible as the cluster size gets large this paper proposes an alternative approach alternating logistic regressions for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios this algorithm iterates between a logistic regression using first order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters for clusters of size n alternating logistic regression involves evaluation and inversion of matrices of order n2 rather than n4 as required for second order generalized estimating equations the alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second order equations in a few problems the new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures

a minimax approach to consistency and efficiency for estimating equations the consistency of estimating equations has been studied in the main along the lines of cramer s classical argument which only asserts the existence of consistent solutions the statement similar to that of doob and wald which identifies the consistent solutions has not yet been established the obstacle is that the solutions of estimating equations cannot in general be defined as the maximum of likelihood functions in this paper we demonstrate that the consistent solutions can be identified as the minimax of a function r whose properties resemble those of a log likelihood ratio but which exists in a much wider context furthermore since we do not need r to be differentiable the minimax is consistent even when the estimating equation does not exist in this respect the minimax is a new estimator we first convey the idea by focusing on the quasi likelihood estimate and then indicate its full generality by providing a set of sufficient conditions for consistency and studying a number of important cases efficiency will also be verified

analysing repeated measurements with possibly missing observations by modelling marginal distributions suppose that subjects are observed repeatedly over a common set of time points with possibly time dependent covariates and possibly missing observations at each time point we model the marginal distribution of the response variable and the effect of the covariates on that distribution using a class of quasi likelihood models studied in mccullagh and nelder no parametric model of dependence of the repeated observations of the subject is assumed for large samples the quasi likelihood estimates of the time specific regression coefficients over the set of predetermined time points are shown to be approximately jointly normal this coupled with various inference procedures provides a global picture about the effects of the covariates on the response variable over the entire study period a lack of fit test for testing the adequacy of the assumed quasi likelihood model is also provided all the methods considered here are illustrated with real life examples

generalized ordinary differential equation models existing estimation methods for ordinary differential equation ode models are not applicable to discrete data the generalized ode gode model is therefore proposed and investigated for the first time we develop the likelihood based parameter estimation and inference methods for gode models we propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving odes the simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ode model estimation approach and the extended smoothing based esb method supplementary materials for this article are available online

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

a deviance function for the quasi likelihood method summary we introduce a deviance function that can be used in conjunction with the quasilikelihood method the need for such functions arises when the quasi log likelihood function is not uniquely defined the deviance is obtained by projecting a pair of centred likelihood ratios onto the direct sum of two hilbert spaces spanned by the observations locally at the null and the alternative hypotheses the deviance function is equivalent to the quasi log likelihood ratio provided that the latter is uniquely defined like the quasilog likelihood ratio it is invariant antisymmetric and linear in the observations it can be defined for both independent and dependent observations in certain situations when the quasi score has multiple roots the confidence set based on the deviance is better than that based on the score test the deviance also induces a divergence measure between two sets of moments which resembles jeffreys divergence between two probability measures

model checking techniques based on cumulative residuals depuis longtemps on utilise les residus pour apprecier graphiquement et muneriquement l adequation de modeles de regression l analyse conventionnelle des residus fondee sur les graphes des residus bruts ou des courbes lissees est eminemment subjective tandis que la plupart des tests numeriques d ajustement informent peu sur la nature de l inadequation nous developpons des techniques d examen d un modele objectives et informatives qui reposent soit sur les sommes des residus cumulees selon certaines coordonnees comme une covariable on le predicteur lineaire soit sur des regroupements partiels sommes ou moyennes mobiles selon ces coordonnees pour une grande variete de modeles statistiques et de structures des observations dont les modeles lineaires generalises sur observations independantes ou correlees les distributions de ces processus stochastiques sous le modele postule peuvent etre approchees par des processus gaussiens centres faciles a simuler on pent done comparer graphiquement et numeriquement chaque processus observe a une serie de realisations du ment chaque processus observe a une serie de realisations du processus gaussien ces comparaisons permettent d evaluer objectivement dans quelle mesure une tendance observee sur un graphique serait attribuable a une mauvaise specification du modele plutot qu aux fluctuations d echantillonnage ces techniques sont particulierement utiles pour l examen de la fonction de lien ou de la forme fonctionnelle d une covariable plusieurs exemples medicaux illustrent cette approche

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

on the exponential model for survival summary a simple sufficient condition for the existence consistency and asymptotic normality of the regression coefficient in the exponential model for survival is given the intuition that consistent estimation can only be guaranteed when censoring variables are not too small depending on the values of the covariates can be quantified in some examples with the use of this condition the exponential model for survival time is a fundamental building block in survival analysis yet there seems to be no easily accessible condition which guarantees existence consistency and asymptotic normality of the estimators well known heuristics such as those of kalbfleisch prentice 1980 p 51 suggest that a sufficient condition will be uniform asymptotic negligibility of the sequence of covariate vectors by comparison with the information matrix we show that this is indeed the case see condition 1 below the simplicity of this condition encourages applications and we demonstrate for example how condition 1 reveals the role of censoring in the consistency of the estimator since an analogue of condition 1 is a necessary and sufficient condition for asymptotic normality of the regression coefficients in the ordinary least squares model eicker 1965 it is probably as general as could be hoped for our method is to extend to the survival context the methods of fahrmeir kaufmann 1985 who in the area of generalized linear models took advantage of the close to linear structure of those models to strengthen traditional asymptotic arguments for general maximum likelihood estimators the asymptotics of survival models have been widely studied using the theory of counting processes and martingales and borgan 1984 uses this theory to deal with a wide class of models with covariates to apply his results borgan 1984 p 14 however very technical conditions involving uniform convergence of various stochastic processes must be verified borgan s methods rely on a traditional approach and cannot yield simple sufficient conditions like condition 1 we need nothing more sophisticated than chebychev s inequality and the central limit theorem for sums of independent random variables although we are restricted to the close to linear exponential model another approach by friedman 1982 requires complex assumptions

exact simultaneous confidence bands for a collection of univariate polynomials in regression analysis we discuss a simple simulation method for construction of exact confidence bands having a pre assigned confidence level simultaneously for several regression functions which are univariate polynomials in the predictors this is accomplished by combining and extending existing results in a manner that permits both finite and infinite ranges for individual predictor variables we illustrate the method for a logistic regression model with both dichotomous and continuous predictors

least median of weighted squares in logistic regression with large strata summary one aim of robust regression is to find estimators with high finite sample breakdown points although various robust estimators have been proposed in logistic regression models their breakdown points are not yet known here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point provided the estimator has to fulfill a weak condition in logistic regression models with large strata however a modification of rousseeuw s least median of squares estimator is shown to have a finite sample breakdown point of approximately 2

restoring discrete painleve equations from an e8 1 associated one we present a systematic method for the construction of discrete painleve equations the method dubbed restoration allows one to obtain all discrete painleve equations that share a common autonomous limit up to homographic transformations starting from any one of those limits as the restoration process crucially depends on the classification of canonical forms for the mappings in the quispel roberts thompson qrt family it can in principle only be applied to mappings that belong to that family however as we show in this paper it is still possible to obtain the results of the restoration even when the initial mapping is not of the qrt type at least for the system at hand but we believe our approach to be of much wider applicability for the equations derived in this paper we also show how starting from a form where the independent variable advances one step at a time one can obtain versions corresponding to multistep evolutions we present a systematic method for the construction of discrete painleve equations the method dubbed restoration allows one to obtain all discrete painleve equations that share a common autonomous limit up to homographic transformations starting from any one of those limits as the restoration process crucially depends on the classification of canonical forms for the mappings in the quispel roberts thompson qrt family it can in principle only be applied to mappings that belong to that family however as we show in this paper it is still possible to obtain the results of the restoration even when the initial mapping is not of the qrt type at least for the system at hand but we believe our approach to be of much wider applicability for the equations derived in this paper we also show how starting from a form where the independent variable advances one step at a time one can obtain versions corresponding to multistep evolutions

an algorithm based on discrete response regression models suitable to correct the bias of non response in surveys with several capture tries the use of survey plans which contemplate several tries or call backs when endeavouring to capture individual data may supply unarguable information in certain sampling situations with non ignorable non response this paper presents an algorithm whose final aim is the estimation of the individual non response probabilities from a general perspective of discrete response regression models which includes the well known probit and logit models it will be assumed that the respondents supply all the variables of interest when they are captured nevertheless the call backs continue even after previous captures for a small number of tries r which has been fixed beforehand only for estimating purposes the different retries or call backs are supposed to be carried out with different capture intensities as mentioned above the response probabilities which may vary from one individual to another are sought by discrete response regression models whose parameters are estimated from conditioned likelihoods evaluated on the respondents only the algorithm quick and easy to implement may be used even when the capture indicator matrix has been partially recorded finally the practical performance of the proposed procedure is tested and evaluated from empirical simulations whose results are undoubtedly encouraging

adaptive prior weighting in generalized regression the prior distribution is a key ingredient in bayesian inference prior information on regression coefficients may come from different sources and may or may not be in conflict with the observed data various methods have been proposed to quantify a potential prior data conflict such as box s p value however there are no clear recommendations how to react to possible prior data conflict in generalized regression models to address this deficiency we propose to adaptively weight a prespecified multivariate normal prior distribution on the regression coefficients to this end we relate empirical bayes estimates of prior weight to box s p value and propose alternative fully bayesian approaches prior weighting can be done for the joint prior distribution of the regression coefficients or under prior independence separately for prespecified blocks of regression coefficients we outline how the proposed methodology can be implemented using integrated nested laplace approximations inla and illustrate the applicability with a bayesian logistic regression model for data from a cross sectional study we also provide a simulation study that shows excellent performance of our approach in the case of prior misspecification in terms of root mean squared error and coverage supplementary materials give details on software implementation and code and another application to binary longitudinal data from a randomized clinical trial using a bayesian generalized linear mixed model

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

wavelet based estimations of fractional brownian sheet least squares versus maximum likelihood abstract the scaling behavior or self similarity and long range dependence has been studied in numerous fields such as computer telecommunication hydrology and economics and can be characterized by the hurst parameter h fractional brownian sheet plays an important role in modeling the scaling behavior in multi dimensional signals a wavelet based maximum likelihood estimator for the hurst parameter h h 1 h d of fractional brownian sheet is proposed it is asymptotically normal and compared with the wavelet based least squares estimators introduced in the previous article from theoretical analysis and numerical simulation the theoretical results show that the proposed estimator has the same asymptotic covariance as the least squares estimator of which the weight is equal to the number of available wavelet coefficients and the convergence rates of two estimators are both o 1 i 1 d t i t i is sample length in the i th dimension the simulation results show that the proposed estimator performs better than the least squares estimators in bias and costs less runtime than the generalized least squares estimator realized by the two step method

asymptotic theory in generalized ilinear models with nuisance scale parameters this paper establishes the asymptotic normality and the consistencyrobustness of the weighted least squares estimator wlse in the generalized linear models with multiple nuisance scale parameters in addition noting that the asymptotic robust statistical inference in presence of nuisance scale parameters requires a consistency robust estimator of the asymptotic covariance matrix of the wlse this paper derives a class of covariance estimators and proves their consistency robustness

sure independence screening in generalized linear models with np dimensionality ultrahigh dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research among others fan and lv 2008 propose an independent screening framework by ranking the marginal correlations they showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with gaussian covariates and responses in this paper we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models we show that the proposed methods with fan and lv 2008 as a very special case also possess the sure screening property with vanishing false selection rate the conditions under which that the independence learning possesses a sure screening is surprisingly simple this justifies the applicability of such a simple method in a wide spectrum we quantify explicitly the extent to which the dimensionality can be reduced by independence screening which depends on the interactions of the covariance matrix of covariates and true parameters simulation studies are used to illustrate the utility of the proposed approaches in addition we supported in part by grant nsf grants dms 0714554 and dms 0704337 the bulk of the work was conducted when rui song was a postdoctoral research fellow at princeton university the authors would like to thank the associate editor and two referees for their constructive comments that improve the presentation and the results of the paper ams 2000 subject classifications primary 68q32 62j12 secondary 62e99 60f10

asymptotics for generalized estimating equations with large cluster sizes generalized estimating equations are used in regression analysis of longitudinal data where observations on each subject are correlated statistical analysis using such methods is based on the asymptotic properties of regression parameter estimators this paper presents asymptotic results when either the number of independent subjects or the cluster sizes the number of observations on each subject or both go to infinity a set of information matrix based general conditions is developed which leads to the weak and strong consistency as well as the asymptotic normality of the estimators most of the results are parallel to the elegant work of fahrmeir and kaufmann on maximum likelihood estimators related to the generalized linear models the conditions for weak consistency and asymptotic normality are verified for several examples of general interest

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

adjusting for nonresponse bias using logistic regression summary a method of adjustment for nonresponse is considered no information about the nonrespondents is required but the respondents are assumed to answer all questions of interest one or more call backs are assumed the probabilities of response are represented by a logistic regression model in which variables in the survey are explanatory variables the probabilities are estimated using a modified conditional maximum likelihood approach based on the respondents the estimated probabilities are used in a horvitzthompson type estimator to reduce bias in the estimation of sample moments simulations suggest that the method reduces the mean squared error of estimation when response probabilities depend strongly on variables in the survey

piecewise exponential models for survival data with covariates a general class of models for analysis of censored survival data with covariates is considered if n individuals are observed over a time period divided into i n intervals it is assumed that lambda j t the hazard rate function of the time to failure of the individual j is constant and equal to lambda ij 0 on the i th interval and that the vector ell log lambda ij j 1 ldots n i 1 ldots i n lies in a linear subspace the maximum likelihood estimate hat ell of ell provides a simultaneous estimate of the underlying hazard rate function and of the effects of the covariates maximum likelihood equations and conditions for existence of hat ell are given the asymptotic properties of linear functionals of hat ell are studied in the general case where the true hazard rate function lambda 0 t is not a step function and i n increases without bound as the maximum interval length decreases in comparison with recent work on regression analysis of survival data the asymptotic results are obtained under more relaxed conditions on the regression variables

on the computation of likelihood ratio and score test based confidence intervals in generalized linear models numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered newton s method appears to have better convergence properties than the secant method in the likelihood ratio test case however the secant method may be easier to program for models with link functions that are not natural similarly the secant method is easier to implement for the computation of score test based intervals the practical implementation of the procedures in glim is illustrated

weighted average least squares estimation of generalized linear models abstract the weighted average least squares wals approach introduced by magnus et al 2010 in the context of gaussian linear models has been shown to enjoy important advantages over other strictly bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors in this paper we extend the wals approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models glms we study the large sample properties of the wals estimator for glms under a local misspecification framework and the finite sample properties of this estimator by a monte carlo experiment the design of which is based on a real empirical analysis of attrition in the first two waves of the survey of health aging and retirement in europe share

bias corrected aic for selecting variables in multinomial logistic regression models abstract in this paper we consider the bias correction of akaike s information criterion aic for selecting variables in multinomial logistic regression models for simplifying a formula of the bias corrected aic we calculate the bias of the aic to a risk function through the expectations of partial derivatives of the negative log likelihood function as a result we can express the bias correction term of the bias corrected aic with only three matrices consisting of the second third and fourth derivatives of the negative log likelihood function by conducting numerical studies we verify that the proposed bias corrected aic performs better than the crude aic

sequential confidence regions for maximum likelihood estimates the goal of this paper is to develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model it is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed sample size procedure it is further shown that the cost of ignorance associated with the sequential procedure is bounded applications are made to estimation problems arising in prospective and retrospective studies

within cluster resampling within cluster resampling is proposed as a new method for analysing clustered data although the focus of this paper is clustered binary data the within cluster resampling asymptotic theory is general for many types of clustered data within cluster resampling is a simple but computationally intensive estimation method its main advantage over other marginal analysis methods such as generalised estimating equations liang zeger 1986 zeger liang 1986 is that it remains valid when the risk for the outcome of interest is related to the cluster size which we term nonignorable cluster size we present theory for the asymptotic normality and provide a consistent variance estimator for the within cluster resampling estimator simulations and an example are developed that assess the finite sample behaviour of the new method and show that when both methods are valid its performance is similar to that of generalised estimating equations

multisample adjusted u statistics that account for confounding covariates multisample u statistics encompass a wide class of test statistics that allow the comparison of 2 or more distributions u statistics are especially powerful because they can be applied to both numeric and nonnumeric data eg ordinal and categorical data where a pairwise similarity or distance like measure between categories is available however when comparing the distribution of a variable across 2 or more groups observed differences may be due to confounding covariates for example in a case control study the distribution of exposure in cases may differ from that in controls entirely because of variables that are related to both exposure and case status and are distributed differently among case and control participants we propose to use individually reweighted data ie using the stratification score for retrospective data or the propensity score for prospective data to construct adjusted u statistics that can test the equality of distributions across 2 or more groups in the presence of confounding covariates asymptotic normality of our adjusted u statistics is established and a closed form expression of their asymptotic variance is presented the utility of our approach is demonstrated through simulation studies as well as in an analysis of data from a case control study conducted among african americans comparing whether the similarity in haplotypes ie sets of adjacent genetic loci inherited from the same parent occurring in a case and a control participant differs from the similarity in haplotypes occurring in 2 control participants

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

estimation of relative risk and prevalence ratio relative risks rrs and prevalence ratios prs are measures of association that are more intuitively interpretable than odds ratios ors many health science studies report or estimates however even when their designs permit and study questions target rrs and or prs this is partially attributable to the popularity and technical advantage i e no restriction on the parameter space of logistic regression for estimating ors to improve this practice several biostatistical approaches for estimating rr pr adjusting for potential confounders have been proposed in this paper we consider two rr pr estimating methods 1 the modification of log binomial regression with the copy method and 2 an inverse probability of treatment weighted iptw log binomial regression we newly propose for the copy method we rigorously establish the existence and uniqueness of the maximum likelihood estimator provided certain degeneracies in the data do not occur moreover the global maximum of the copy modified likelihood is shown to occur at an interior point of the restricted parameter space this result explains why the copy method avoids convergence problems of log binomial models frequently for the iptw estimator we show that its simple procedure results in standardized estimates of rr pr and discuss its potential challenges extensions and an improvement through propensity score based grouping of observations furthermore we compare the performances of four rr pr estimation methods including the copy method and iptw log binomial regression on simulated data we demonstrate a lack of robustness of the copy method against misspecification of the true relationship between binary outcome and explanatory variables and show robustness of the iptw approach in this regard

using the jackknife for estimation in log link bernoulli regression models bernoulli or binomial regression using a generalized linear model with a log link function where the exponentiated regression parameters have interpretation as relative risks is often more appropriate than logistic regression for prospective studies with common outcomes in particular many researchers regard relative risks to be more intuitively interpretable than odds ratios however for the log link when the outcome is very prevalent the likelihood may not have a unique maximum to circumvent this problem a copy method has been proposed which is equivalent to creating for each subject an additional observation with the same covariates except the response variable has the outcome values interchanged 1 s changed to 0 s and 0 s changed to 1 s the original response is given weight close to 1 while the new observation is given a positive weight close to 0 this approach always leads to convergence of the maximum likelihood algorithm except for problems with convergence due to multicollinearity among covariates even though this method produces a unique maximum when the outcome is very prevalent and or the sample size is relatively small the copy method can yield biased estimates here we propose using the jackknife as a bias reduction approach for the copy method the proposed method is motivated by a study of patients undergoing colorectal cancer surgery copyright 2014 john wiley sons ltd

renewable estimation and incremental inference in generalized linear models with streaming data sets the paper presents an incremental updating algorithm to analyse streaming data sets using generalized linear models the method proposed is formulated within a new framework of renewable estimation and incremental inference in which the maximum likelihood estimator is renewed with current data and summary statistics of historical data our framework can be implemented within a popular distributed computing environment known as apache spark to scale up computation consisting of two data processing layers the rho architecture enables us to accommodate inference related statistics and to facilitate sequential updating of the statistics used in both estimation and inference we establish estimation consistency and asymptotic normality of the proposed renewable estimator in which the wald test is utilized for an incremental inference our methods are examined and illustrated by various numerical examples from both simulation experiments and a real world data analysis

optimal designs for the rasch model in this paper optimal designs will be derived for estimating the ability parameters of the rasch model when difficulty parameters are known it is well established that a design is locally d optimal if the ability and difficulty coincide but locally optimal designs require that the ability parameters to be estimated are known to attenuate this very restrictive assumption prior knowledge on the ability parameter may be incorporated within a bayesian approach several symmetric weight distributions e g uniform normal and logistic distributions will be considered furthermore maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

estimation of current reliability in a duane based reliability growth model in this article i investigate the statistical inference concerning the current field stage reliability of a reliability growth model the model assuming a step intensity structure evolves from the physical consideration of the duane learning curve property and incorporates the effect of a testanalyze and fix program that is typically undertaken in a developmental testing program both exact and large sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity under the assumption that the step intensity model represents the reality i provide an assessment of the extent of misspecification when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures extensive simulation results are carried out to supplement the theoretical findings an illustration with a dataset is provided as a demonstration of the application of the inference results

asymptotic results with generalized estimating equations for longitudinal data we consider the marginal models of liang and zeger biometrika 73 1986 13 22 for the analysis of longitudinal data and we develop a theory of statistical inference for such models we prove the existence weak consistency and asymptotic normality of a sequence of estimators defined as roots of pseudo likelihood equations

concavity and estimation on donne des conditions simplifiees pour la consistance et la normalite asymptotique d estimations m deduites par maximisation de moyennes de fonctions concaves aleatoires identiquement distribuees et independantes des applications sont donnees pour l estimation de maximum de vraisemblance