nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

analysis of embryonic development with a model for under or overdispersion relative to binomial variation summary observations from a study of the development of ovulations into embryos for texel sheep are analysed with a model for count data that are under or overdispersed relative to binomial variation the analysis is based on maximum quasi likelihood mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall following an approach suggested by williams 1982 applied statistics 31 144 148 the dispersion parameter is developed as a combination of a variance component representing shared maternal effects and a correlation typically negative between ovulations within ewes the number of ovulations the binomial denominator is included as an explanatory variable

tensor notation and cumulants of polynomials a modified and extended tensor notation is introduced that is sufficient to cover multivariate moments and cumulants as special cases using this notation two basic identities are given the first of these expresses generalized cumulants in terms of ordinary cumulants the second gives the joint cumulant generating function of any polynomial transformation in terms of the cumulants of the original variables three applications of the basic identities are given the first application is concerned with sample cumulants or k statistics the second to edgeworth series and the third to exponential family models

a network algorithm for performing fisher s exact test in r c contingency tables abstract an exact test of significance of the hypothesis that the row and column effects are independent in an r c contingency table can be executed in principle by generalizing fisher s exact treatment of the 2 2 contingency table each table in a conditional reference set of r c tables with fixed marginal sums is assigned a generalized hypergeometric probability the significance level is then computed by summing the probabilities of all tables that are no larger on the probability scale than the observed table however the computational effort required to generate all r c contingency tables with fixed marginal sums severely limits the use of fisher s exact test a novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here the problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length some interesting new optimization theorems are developed in the process the numer

bias reduction in exponential family nonlinear models in firth 1993 biometrika it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector and that in canonical link generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data here a more general family of bias reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models the resulting formulae for the adjusted score vector are computationally convenient and in univariate models they directly suggest implementation through an iterative scheme of data adjustment for generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method an illustrative application to the goodman row column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models

goodness of fit of generalized linear models to sparse data we derive approximations to the first three moments of the conditional distribution of the deviance statistic for testing the goodness of fit of generalized linear models with non canonical links by using an estimating equations approach for data that are extensive but sparse a supplementary estimating equation is proposed from which the modified deviance statistic is obtained an application of a modified deviance statistic is shown to binomial and poisson data we also conduct a performance study of the modified pearson statistic derived by farrington and the modified deviance statistic derived in this paper in terms of size and power through a small scale simulation experiment both statistics are shown to perform well in terms of size the deviance statistic however shows an advantage of power two examples are given

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

outliers and residual distributions in logistic regression abstract detection of outliers and other diagnostics based on residuals have gained widespread use in linear regression logistic regression has been both blessed and hindered by this development certainly logistic regression requires procedures to detect global and local model weaknesses thus the wealth of work done in linear regression provides guides and suggestions that may with care and ingenuity be applied to logistic regression several innovative attempts in this direction have been made by authors such as tsiatis 1980 pregibon 1979 1981 landwehr pregibon and shoemaker 1984 and cook and weisberg 1982 unfortunately the similarities that allow such techniques to adapt to logistic regression seem in addition to hide many of the differences two such differences are discussed here the first examines the effect of events of small probability on estimation in logistic regression the simple conclusion is that to estimate the probability of success p in an area in which p is small

global regular solutions of second order hamilton jacobi equations in hilbert spaces with locally lipschitz nonlinearities abstract this paper is devoted to the study of a second order hamilton jacobi equation in infinite dimensions with a locally lipschitz continuous hamiltonian h related with a stochastic optimal control problem driven by white noise in an earlier paper the author studied the case of globally lipschitz continuous hamiltonian h this paper is concerned with the case of locally lipschitz continuous h that include e g the quadratic case which appears very frequently in the applications existence uniqueness and c 2 regularity of a local solution follow by methods given previously the heart of the work is the proof of a priori estimates of the c 1 norm of the local solution this has been done by studying properties of nonlinear transition semigroups and by a careful application of them to our problem the results have been applied to a stochastic optimal control problem proving existence of feedback optimal controls

exact person fit indexes for the rasch model for arbitrary alternatives a new algorithm for obtaining exact person fit indexes for the rasch model is introduced which realizes most powerful tests for a very general family of alternative hypotheses including tests concerning dif as well as model deviating item correlations the method is also used as a goodness of fit test for whole data sets where the item parameters are assumed to be known for tests with 30 items at most exact values are obtained for longer tests a monte carlo algorithm is proposed simulated examples and an empirical investigation demonstrate test power and applicability to item elimination

goodness of fit tests for log linear models in sparse contingency tables abstract the asymptotic normality of the likelihood ratio goodness of fit statistic is demonstrated for testing the fit of log linear models with closed form maximum likelihood estimates in sparse contingency tables unlike the traditional chi squared theory the number of categories in the table increases as the sample size increases but not all of the expected frequencies are required to become large some results of a small monte carlo study are presented the traditional chi squared approximation is reasonably accurate for the pearson statistic for many sparse tables but cases are presented for which it fails the normal approximation can be much more accurate than the chi squared approximation for the likelihood ratio statistic but the bias of estimated moments is a potential problem for very sparse tables

practical use of higher order asymptotics for multiparameter exponential families recently developed asymptotics based on saddlepoint methods provide important practical methods for multiparameter exponential families especially in generalized linear models the aim here is to clarify and explore these attention is restricted to tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family excellent approximations to exact conditional inferences are often available in terms of simple adjustments to the signed square root of the likelihood ratio statistic

optimal control of a stochastic delay heat equation with boundary noise and boundary control in this paper a controlled stochastic delay heat equation with neumann boundary noise and boundary control is considered the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of the backward stochastic differential equations which is applied to the optimal control problem

methods for exact goodness of fit tests abstract numerous goodness of fit tests with asymptotic chi squared distributions have been proposed for discrete multivariate data and there has been much discussion about using asymptotic results for computing critical values when there are small expected cell values although exact methods would be preferred in these situations it generally is believed that such methods are computationally intractable we propose methods for calculating exact distributions and significance levels for goodness of fit statistics that are computationally feasible over a wide range of models in particular the distribution for a simple multinomial model can be evaluated in polynomial time for composite null hypotheses we calculate the distribution conditional on the sufficient statistics for the nuisance parameters we calculate the characteristic function of a distribution and invert the characteristic function using the fast fourier transform fft our approach emphasizes the relationship between exact methods and

a comparison of three simple test theory models in very simple test theory models such as the rasch model a single parameter is used to represent the ability of any examinee or the difficulty of any item simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available and are themselves of real practical value for small or even medium samples they can also serve a normative role in test design as an alternative to the rasch model or the rasch model with a correction for guessing a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference this model provides a natural account of guessing and has other useful things to contribute as well it also offers an alternative to the rasch model with the usual correction for guessing the three models are compared in terms of statistical properties and fits to actual data the goal of the paper is to widen the range of minimal models available to test analysts

a note on the computation of the second order derivatives of the elementary symmetric functions in the rasch model jansen 1984 gave explicit formulas for the computation of the second order derivatives of the elementary symmetric functions but they are only applicable to those pairs of items which have unequal parameters it is shown here that for equal parameters similar explicit formulas do exist too facilitating the application of the newton raphson procedure to estimate the parameters in the rasch model and related models according to the conditional maximum likelihood principle

behaviour of third order terms in quadratic approximations of lr statistics in multivariate generalized linear models on presente des bornes d erreurs globales pour des modeles logit et log lineaire et des modeles dependant de la loi gamma

outlier tests for logistic regression a conditional approach summary we consider exact conditional methods for identifying outliers in logistic regression data tests for a single outlier and multiple outliers are developed assuming a logistic slippage model the p values for these tests are determined using an explicit enumeration of all possible responses consistent with the observed value of the sufficient statistic justifications are given for preferring this computationally intensive approach to standard methods based on asymptotic approximations the techniques are applied to two examples

jackknifing and bootstrapping goodness of fit statistics in sparse multinomials abstract many goodness of fit problems can be put in the following form n n 1 nk is a multinomial n vector and it is desired to test the composite null hypothesis h 0 p against all possible alternatives the usual tests used are pearson s 1900 statistic or the likelihood ratio statistic neyman and pearson 1928 cressie and read 1984 pointed out that both of these statistics are in the power family of statistics with 1 and 0 respectively they suggested an alternative statistic with although all of these statistics are asymptotically 2 in the usual situation of k fixed and n this is not the case if the multinomial is sparse specifically morris 1975 showed that under certain regularity conditions with k and n both x 2 and g 2 are asymptotically normal with different mean and variance under a simple null hypothesis cressie and read 1984 extended these results to the general 2ni family although these results have not been proven for composite nul

constructing exact significance tests with restricted randomization rules summary in a clinical trial comparing two treatments suppose that subjects are assigned sequentially to the treatment groups by a restricted randomization rule under the randomization model an efficient recursive algorithm is provided to generate the exact permutational distribution for linear rank statistics given the final imbalance between the number of patients in the two groups if only the significance level of the test is required the efficiency of the algorithm can be improved significantly in general by the time the size of the trial reaches 30 the large sample approximation to the permutation distribution wei smythe smith 1986 is satisfactory the new procedure is illustrated by censored survival data from a prostatic cancer clinical trial we show that if the study subjects are not a random sample from a well defined population then the treatment allocation rule used at the design stage should not be ignored in the analysis

constructing the exact significance level for a person fit statistic this paper uses an extension of the network algorithm originally introduced by mehta and patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the rasch model by assuming that item difficulties are known the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score a simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

stochastic optimal control problems and parabolic equations in banach spaces we consider stochastic optimal control problems in banach spaces these problems are related to nonlinear controlled equations with dissipative nonlinearity and are treated via the backward stochastic differential equation approach which also allows us to solve in a mild sense hamilton jacobi bellman equations in banach spaces we apply the results to controlled stochastic heat and wave equations with a cost functional that is well defined on continuous functions and to delay equations in spaces of p integrable functions

existence and uniqueness of c n almost periodic solutions to some ordinary differential equations abstract in this paper we prove the existence and uniqueness of c n almost periodic solutions to the ordinary differential equation x t a t x t f t t r where the matrix a t r m k c is periodic and f r c k is c n almost periodic we also prove the existence and uniqueness of an ultra weak c n almost periodic solution in the case when a t a is independent of t finally we prove also the existence and uniqueness of a mild c n almost periodic solution of the semilinear hyperbolic equation x t a x t f t x considered in a banach space assuming f t x is c n almost periodic in t for each x x satisfies a global lipschitz condition and takes values in an extrapolation space f a 1 associated to a

bayes modal estimation in item response models this article describes a bayesian framework for estimation in item response models with two stage prior distributions on both item and examinee populations strategies for point and interval estimation are discussed and a general procedure based on the em algorithm is presented details are given for implementation under one two and three parameter binary logistic irt models novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest improved estimation in a moderately small sample is demonstrated with simulated data

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

weighted pseudo almost periodic functions and applications to evolution equations with delay in this paper we introduce a new class of vector valued weighted pseudo almost periodic functions and present some basic properties about these new functions moreover we obtain an new existence theorem of vector valued weighted pseudo almost periodic solution to the evolution equations x t ax t f t x t with delay in a banach space x

extensions of the partial credit model the partial credit model developed by masters 1982 is a unidimensional latent trait model for responses scored in two or more ordered categories in the present paper some extensions of the model are presented first a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters secondly two statistical tests for evaluating model fit are presented the former test has power against violation of the assumption about the ability distribution the latter test offers the possibility of identifying specific items that do not fit the model

operator norm inequalities between tensor unfoldings on the partition lattice interest in higher order tensors has recently surged in data intensive fields with a wide range of applications including image processing blind source separation community detection and feature extraction a common paradigm in tensor related algorithms advocates unfolding or flattening the tensor into a matrix and applying classical methods developed for matrices despite the popularity of such techniques how the functional properties of a tensor changes upon unfolding is currently not well understood in contrast to the body of existing work which has focused almost exclusively on matricizations we here consider all possible unfoldings of an order k tensor which are in one to one correspondence with the set of partitions of 1 k we derive general inequalities between the lp norms of arbitrary unfoldings defined on the partition lattice in particular we demonstrate how the spectral norm p 2 of a tensor is bounded by that of its unfoldings and obtain an improved upper bound on the ratio of the frobenius norm to the spectral norm of an arbitrary tensor for specially structured tensors satisfying a generalized definition of orthogonal decomposability we prove that the spectral norm remains invariant under specific subsets of unfolding operations

natural statistics for spectral samples spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors this parallel extends to symmetric functions k statistics and polykays we construct spectral k statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

analysis of multiple partially ordered responses to belief items with don t know option understanding beliefs values and preferences of patients is a tenet of contemporary health sciences this application was motivated by the analysis of multiple partially ordered set poset responses from an inventory on layman beliefs about diabetes the partially ordered set arises because of two features in the data first the response options contain a don t know dk option and second there were two consecutive occasions of measurement as predicted by the common sense model of illness beliefs about diabetes were not necessarily stable across the two measurement occasions instead of analyzing the two occasions separately we studied the joint responses across the occasions as a poset response few analytic methods exist for data structures other than ordered or nominal categories poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data leading to the loss of nuanced information that might be present within poset categories in this paper we developed a general class of item response models for analyzing the poset data collected from the common sense model of diabetes inventory the inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model to apply an item response model to the poset diabetes inventory we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard irt software could be directly used for the purpose of item estimation and individual scoring simulation experiments were used to examine parameter recovery for the proposed poset model

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

on assessing goodness of fit of generalized linear models to sparse data summary approximations to the first three moments of pearson s statistic are obtained for noncanonical generalized linear models extending the results of mccullagh a first order modification to pearson s statistic is proposed which induces local orthogonality with the regression parameters resulting in substantial simplifications and increased power accurate and easily computed approximations to the moments of the modified pearson statistic conditional on the estimated regression parameters are obtained for testing goodness of fit to sparse data both the pearson statistic and its modification are shown to be asymptotically independent of the regression parameters simulation studies and examples are given

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

higher order asymptotics and its application to testing the equality of the examinee ability over two sets of items in educational and psychological measurement researchers and or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items such problems can arise in measurement of change detection of cheating on unproctored tests erasure analysis detection of item preknowledge etc traditional frequentist approaches that are used in such problems include the wald test the likelihood ratio test and the score test e g fischer appl psychol meas 27 3 26 2003 finkelman weiss kim kang appl psychol meas 34 238 254 2010 glas dagohoy psychometrika 72 159 180 2007 guo drasgow int j sel assess 18 351 364 2010 klauer rettig br j math stat psychol 43 193 206 1990 sinharay j educ behav stat 42 46 68 2017 this paper shows that approaches based on higher order asymptotics e g barndorff nielsen cox inference and asymptotics springer london 1994 ghosh higher order asymptotics institute of mathematical statistics hayward 1994 can also be used to test for the equality of the examinee ability over two sets of items the modified signed likelihood ratio test e g barndorff nielsen biometrika 73 307 322 1986 and the lugannani rice approximation lugannani rice adv appl prob 12 475 490 1980 both of which are based on higher order asymptotics are shown to provide some improvement over the traditional frequentist approaches in three simulations two real data examples are also provided

sampling for conditional inference on case control data summary the problem of exact conditional inference for discrete multivariate case control data has two forms the first is grouped case control data where monte carlo computations can be done using the importance sampling method of booth and butler 1999 biometrika86 321 332 or a proposed alternative sequential importance sampling method the second form is matched case control data for this analysis we propose a new exact sampling method based on the conditional poisson distribution for conditional testing with one binary and one integral ordered covariate this method makes computations on data sets with large numbers of matched sets fast and accurate we provide detailed derivation of the constraints and conditional distributions for conditional inference on grouped and matched data the methods are illustrated on several new and old data sets

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

the many null distributions of person fit indices this paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of rasch contrary to the standard analysis of the rasch model where all persons are kept in the analysis and badly fittingitems may be removed this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the rasch model such persons are called anomalous or aberrant from the response vectors consisting ofk symbols each equal to 0 or 1 it is desired to classify each respondent as either anomalous or as conforming to the model as this model is probabilistic such a classification will possibly involve false positives and false negatives both for the rasch model and for other item response models the literature contains several proposals for a person fit index which expresses for each individual the plausibility that his her behavior follows the model the present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model this distribution however turns out to be rather different for different values of the person s latent trait value this value will be called ability parameter although our results are equally valid for rasch scales measuring other attributes

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

a person fit test for irt models for polytomous items a person fit test based on the lagrange multiplier test is presented for three item response theory models for polytomous items the generalized partial credit model the sequential model and the graded response model the test can also be used in the framework of multidimensional ability parameters it is shown that the lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account the lagrange multiplier statistic has an asymptotic 2 distribution the type i error rate and power are investigated using simulation studies results show that test statistics that ignore the effects of estimation of the persons ability parameters have decreased type i error rates and power incorporating a correction to account for the effects of the estimation of the persons ability parameters results in acceptable type i error rates and power characteristics incorporating a correction for the estimation of the item parameters has very little additional effect it is investigated to what extent the three models give comparable results both in the simulation studies and in an example using data from the neo personality inventory revised

stochastic equations with delay optimal control via bsdes and regular solutions of hamilton jacobi bellman equations we consider an ito stochastic differential equation with delay driven by brownian motion whose solution by an appropriate reformulation defines a markov process x with values in a space of continuous functions mathbf c with generator mathcal l we then consider a backward stochastic differential equation depending on x with unknown processes y z and we study properties of the resulting system in particular we identify the process z as a deterministic functional of x we next prove that the forward backward system provides a suitable solution to a class of parabolic partial differential equations on the space mathbf c driven by mathcal l and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects we also include applications to optimal stochastic control of differential equation with delay in particular we characterize optimal controls as feedback laws in terms of the process x

k statistics and dispersion effects in regression on donne deux ensembles d estimateurs sans biais pour le cas ou la reponse moyenne depend lineairement de covariables connues

optimal control problems for stochastic delay evolution equations in banach spaces we consider the optimal control for a banach space valued stochastic delay evolution equation the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of backward stochastic differential equations an application to optimal control of stochastic delay partial differential equations is also given

normal goodness of fit tests for multinomial models with large degrees of freedom abstract goodness of fit tests for independent multinomials with parameters to be estimated are usually based on pearson s x 2 or the likelihood ratio g 2 both are included in the family of power divergence statistics sd for increasing sample sizes each sd has an asymptotic x 2 distribution provided that the number of cells remains fixed we are dealing with an increasing cells approach where the number j of independent multinomials increases while the number of classes for each multinomial and the number of parameters remain fixed extending results on x 2 and g 2 the asymptotic normality of any sd is obtained for increasing cells the corresponding normal goodness of fit tests discussed here apply for models with large degrees of freedom with no restrictions imposed on the sizes n j of each multinomial allowing large as well as small expectations sparse data within each cell the asymptotic expectation and variance of sd are easy to compute for pearson s x 2 and simplify considerably for

extensions of the concept of local ancillarity summary cox 1980 introduced a notion of local ancillarity in this paper a qth order local ancillary variable is defined the idea of local ancillarity for the multiparameter model with no nuisance parameters is developed for inference and third order local ancillarity is examined in the single parameter model

asymptotic null distribution of person fit statistics with estimated person parameter person fit statistics are considered for dichotomous item response models the asymptotic null distribution is derived for statistics which are linear in the item responses and in which the ability parameter is replaced by an estimate this allows the asymptotically correct standardization of linear person fit statistics with estimated ability parameter the fact that the ability parameter is estimated usually decreases the asymptotic variance

higher order approximations for testing neglected nonlinearity we illustrate the need to use higher order specifically sixth order expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity the test statistic is a quasi likelihood ratio qlr statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activation function violating the no zero condition in cho ishida and white 2011 this statistic is also shown to be asymptotically equivalent under the null to the lagrange multiplier lm statistic of luukkonen saikkonen and terasvirta 1988 and terasvirta 1994 in addition we compare the power properties of our qlr test to one satisfying the no zero condition and find that the latter is not consistent for detecting a dgp with neglected nonlinearity violating an analogous no zero condition whereas our qlr test is consistent

the ump exact test and the confidence interval for person parameters in irt models in educational and psychological measurement when short test forms are used the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold as a result hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic inferences based on the exact distribution on the other hand do not suffer from this limitation however the computation involved for the exact distribution approach is often prohibitively expensive in this paper we propose a general framework for constructing hypothesis tests and confidence intervals for irt models within the exponential family based on exact distribution in addition an efficient branch and bound algorithm for calculating the exact p value is introduced the type i error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation we also demonstrate its practical use by analyzing three real data sets

a comparison of goodness of fit tests for the logistic regression model recent work has shown that there may be disadvantages in the use of the chi square like goodness of fit tests for the logistic regression model proposed by hosmer and lemeshow that use fixed groups of the estimated probabilities a particular concern with these grouping strategies based on estimated probabilities fitted values is that groups may contain subjects with widely different values of the covariates it is possible to demonstrate situations where one set of fixed groups shows the model fits while the test rejects fit using a different set of fixed groups we compare the performance by simulation of these tests to tests based on smoothed residuals proposed by le cessie and van houwelingen and royston a score test for an extended logistic regression model proposed by stukel the pearson chi square and the unweighted residual sum of squares these simulations demonstrate that all but one of royston s tests have the correct size an examination of the performance of the tests when the correct model has a quadratic term but a model containing only the linear term has been fit shows that the pearson chi square the unweighted sum of squares the hosmer lemeshow decile of risk the smoothed residual sum of squares and stukel s score test have power exceeding 50 per cent to detect moderate departures from linearity when the sample size is 100 and have power over 90 per cent for these same alternatives for samples of size 500 all tests had no power when the correct model had an interaction between a dichotomous and continuous covariate but only the continuous covariate model was fit power to detect an incorrectly specified link was poor for samples of size 100 for samples of size 500 stukel s score test had the best power but it only exceeded 50 per cent to detect an asymmetric link function the power of the unweighted sum of squares test to detect an incorrectly specified link function was slightly less than stukel s score test we illustrate the tests within the context of a model for factors associated with low birth weight

a person fit index for polytomous rasch models latent class models and their mixture generalizations a normally distributed person fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution irt models for dichotomous and polytomous data this article extends previous work on the null distribution of person fit indices for the dichotomous rasch model to a number of models for categorical data a comparison of two different approaches to handle the skewness of the person fit index distribution is included

unbiased estimators of ability parameters of their variance and of their parallel forms reliability given known item parameters unbiased estimators are derived i for an examinee s ability parameter and for his proportion correct true score ii for the variances of and across examinees in the group tested and iii for the parallel forms reliability of the maximum likelihood estimator hat theta

approximating the conditional distribution of person fit indexes for checking the rasch model we present a simple approximation to the conditional distribution of goodness of fit statistics for the rasch model assuming that the item difficulties are known the approximation is easily programmed and gives relatively accurate assessments of conditionalp values for tests of length 10 or more a few generalizations are discussed

invariants and likelihood ratio statistics because the likelihood ratio statistic is invariant under reparameterization it is possible to make a large sample expansion of the statistic itself and of its expectation in terms of invariants in particular the bartlett adjustment factor can be expressed in terms of invariant combinations of cumulants of the first two log likelihood derivatives such expansions are given first for a scalar parameter and then for vector parameters geometrical interpretation is given where possible and some special cases discussed

second order hamilton jacobi equations in infinite dimensions some second order hamilton jacobi equations connected to stochastic optimal control problems for infinite dimensional systems driven by a white noise are studied a direct method to prove existence and uniqueness of mild solutions is developed then this solution is identified as the value function of the related stochastic control problem and a feedback formula for optimal controls is derived

asymptotically correct standardization of person fit statistics beyond dichotomous items the l z statistic drasgow et al in br j math stat psychol 38 67 86 1985 is one of the most popular person fit statistics armstrong et al in pract assess res eval 12 16 1 10 2007 snijders psychometrika 66 331 342 2001 derived the asymptotic null distribution of l z when the examinee ability parameter is estimated he also suggested the l z statistic which is the asymptotically correct standardized version of l z however snijders psychometrika 66 331 342 2001 only considered tests with dichotomous items in this paper the asymptotic null distribution of l z is derived for mixed format tests those that include both dichotomous and polytomous items the asymptotically correct standardized version of l z which can be considered as the extension of l z to such tests is suggested the type i error rate and power of the suggested statistic are examined from several simulated datasets the suggested statistic is computed using a real dataset the suggested statistic appears to be a satisfactory tool for assessing person fit for mixed format tests

the existence and uniqueness of the solution for nonlinear kolmogorov equations abstract by means of backward stochastic differential equations the existence and uniqueness of the mild solution are obtained for the nonlinear kolmogorov equations associated with stochastic delay evolution equations applications to optimal control are also given

exact and best confidence intervals for the ability parameter of the rasch model a commonly used method to evaluate the accuracy of a measurement is to provide a confidence interval that contains the parameter of interest with a given high probability smallest exact confidence intervals for the ability parameter of the rasch model are derived and compared to the traditional asymptotically valid intervals based on the fisher information tables of the exact confidence intervals termed clopper pearson intervals can be routinely drawn up by applying a computer program designed by and obtainable from the author these tables are particularly useful for tests of only moderate lengths where the asymptotic method does not provide valid confidence intervals

the conditional distribution of goodness of fit statistics for discrete data abstract i consider the distribution of pearson s statistic and of the likelihood ratio goodness of fit statistic for discrete data in the important case where the data are extensive but sparse it is argued that the appropriate reference distribution is conditional on the sufficient statistic for the unknown regression parameters the first three conditional asymptotic cumulants are derived by edgeworth expansion and these are used for the computation of tail probabilities the principal advantage of the limit considered here as opposed to the more usual x 2 limit is that the cell counts need not be large

likelihood and observed geometries a partir du point de vue de la conditionnalite on etablit un parallele observe a la theorie de chentsov efron amari etc en utilisant l information observee et un tenseur d asymetrie observee

exact inference for contingency tables with ordered categories abstract this article proposes an efficient numerical algorithm for small sample exact inferences in contingency tables having ordinal classifications the inferences which apply conditional on the observed marginal totals also provide an exact analysis for the log linear model of linear by linear association for cell probabilities an exact test of independence has a one sided p value equal to the null probability that model based maximum likelihood estimates of odds ratios are at least as large as the observed estimates the conditional nonnull distribution yields confidence intervals for odds ratios having a linear by linear structure the computations utilize an extension of the network algorithm proposed by mehta and patel 1983

monte carlo exact conditional tests for log linear and logistic models summary the form of the exact conditional distribution of a sufficient statistic for the interest parameters given a sufficient statistic for the nuisance parameters is derived for a generalized linear model with canonical link general results for log linear and logistic models are given a gibbs sampling approach for generating from the conditional distribution is proposed which enables monte carlo exact conditional tests to be performed examples include tests for goodness of fit of the all two way interaction model for a 28 table and of a simple logistic model tests against non saturated alternatives are also considered

an empirical assessment of saddlepoint approximations for testing a logistic regression parameter saddlepoint methods provide quick and easy approximations to significance levels for conditional tests of logistic regression parameters we evaluate the accuracies of saddlepoint approximations for three well known conditional tests bartlett s test for no three factor interaction in a 2 x 2 x 2 table the test for trend in a series of probabilities and the exact test of no association in stratified 2 x 2 tables with a common odds ratio general recommendations are suggested regarding the use of saddlepoint approximations for exact conditional significance levels

an exact and optimal standardized person test for assessing consistency with the rasch model the rasch model predicts that an individual s ability level is invariant over subtests of the total test and thus all subtests measure the same latent trait a person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic given a particular level of ability does not depend on the absolute value of the examinee s ability parameter the test can be routinely performed by applying a computer program designed by and obtainable from the author finally a suboptimal test is derived that is extremely easy to use and an overall group test of the invariance hypothesis discussed all tests considered do not rely on asymptotic approximations hence they may be applied when the test is of only moderate length and the group of examinees is small

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

path dependent hamilton jacobi equations in infinite dimensions abstract we propose notions of minimax and viscosity solutions for a class of fully nonlinear path dependent pdes with nonlinear monotone and coercive operators on hilbert space our main result is well posedness existence uniqueness and stability for minimax solutions a particular novelty is a suitable combination of minimax and viscosity solution techniques in the proof of the comparison principle one of the main difficulties the lack of compactness in infinite dimensional hilbert spaces is circumvented by working with suitable compact subsets of our path space as an application our theory makes it possible to employ the dynamic programming approach to study optimal control problems for a fairly general class of delay evolution equations in the variational framework furthermore differential games associated to such evolution equations can be investigated following the krasovski subbotin approach similarly as in finite dimensions

deviance residuals and normal scores plots summary we discuss the use of normal order statistics plots based on deviance residuals to check distributional assumptions in regression models continuous and discrete error distributions are considered as are censored data misspecified error distributions and discrimination between competing models are discussed with an example residual plots to detect inadequacies in normal linear regression models have a long history an example is the normal scores or rankit plot a plot of ordered residuals against normal order statistics which is used to detect outliers and to check distributional assumptions under or overdispersion in such a plot may also indicate a misspecified systematic component of the model the purpose of this paper is to discuss such plots for regressions with nonnormal errors such as generalized linear models for which deviance residuals are commonly used deviance residuals are known to be approximately normal in many cases in this paper we briefly describe the properties of rankit plots based on them for continuous distributions outline analogous results for discrete and censored data and describe a method for discriminating between competing models with different error distributions most roads lead to rome for the normal distribution in the sense that many definitions of residuals are functions of y jt o not so for other distributions for which various

assessing the fit of the logistic regression model to individual matched sets of case control data we develop exact conditional methods for checking the fit of a logistic regression model to individual matched sets in case control studies justifications are given for preferring this approach to conventional maximum likelihood based methods data from two studies are used to illustrate the techniques

a modified score test statistic having chi squared distribution to order n 1 summary we give a general modified score test statistic whose nuil distribution is chi squared to order n 1 where n is the sample size the modified statistic depends on the joint cumulants of log likelihood derivatives for the full data some applications are discussed following cox reid 1987a we also derive a general formula for bartlett type corrections to improve test statistics whose null asymptotic distributions are chi squared

existence results for some higher order evolution equations with operator coefficients abstract in this paper we study and obtain the existence of c r pseudo almost automorphic solutions to some higher order differential equations with operator coefficients whose forcing is c s pseudo almost automorphic we next use these abstract results to study the existence of c r pseudo almost automorphic solutions to some second order differential equations in hilbert space which among other things model the so called linear beam equation

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

a latent trait model for dichotomous choice data the parella model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences the data analyzed are the dichotomous responses of persons to stimuli with a one zero indicating agreement disagreement with the content of the stimulus the model provides a unidimensional representation of persons and items the response probabilities are a function of the distance between person and stimulus the smaller the distance the larger the probability that a person will agree with the content of the stimulus an estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated