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

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

an asymptotic limit law with a singularly perturbed drift and a random noise an asymptotic stochastic initial value problem with a random microscale superposed upon a deterministic macroscale is considered in this article we derive and prove a limit theorem for the random problem with a rapidly varying deterministic component the asymptotic character of the stochastic initial value problem with a small parameter is realized by solving a final value problem of which the infinitesimal generator consists of a singularly perturbed deterministic component and a random fluctuation intensity component we also give an estimate for the error in the asymptotic approximation in terms of the small parameter this abstract limit theorem is reduced to a limit theorem for the stochastic processes solving a system of stochastic differential equations the corresponding infinitesimal generator of the kolmogorov fokker planck equation is obtained in an asymptotic form and demonstrates how an effective driving force couples with a zero mean random perturbation in both drift and diffusion coefficients our theorem provides a characterization of random noise for evanescent waves in a layered random medium

saddlepoint approximations for the generalized variance and wilks statistic saddlepoint approximations to densities of sums of random variables were introduced by daniels 1954 these methods were further developed by barndorff nielsen cox 1979 to approximate joint and conditional densities for canonical sufficient statistics in exponential family settings approximations for the cumulative distributions of sums were developed by lugannani rice 1980 and robinson 1982 while the approximation of conditional cumulative distribution functions was addressed by skovgaard 1987 the modifications necessary to apply the lugannani rice and skovgaard approximations to conditional distributions of canonical sufficient statistics in exponential family settings have been summarized by davison 1988 reid 1988 provides an overall review of the saddlepoint literature in the present paper the lugannani rice and skovgaard approximations are used to reproduce the distributions of the generalized variance and wilks likelihood ratio statistic in a multivatiate analysis of variance representing the degree of freedom in a gamma regression model as an appropriate linear function the generalized variance distribution arises as the marginal distribution of a canonical sufficient statistic to which the lugannani rice approximation may be applied the more recent approximations of fraser 1990 and barndorff nielsen 1990 are exactly the same for this setting comparison of its accuracy with the approximation of hoel 1937 as well as a normal approximation johnson kotz 1972 p 198 shows the lugannani rice approximation to be highly accurate and uniformly better than its competitors the distribution of wilks likelihood ratio statistic has two distinct characterizations in terms of products of independent beta variates anderson 1958 ch 8 in conjunction with these characterizations we use skovgaard s approximation to construct two distinct

characterizations of the subdifferential of convex integral functions under qualification conditions abstract this work provides formulae for the e subdifferential of integral functions in the framework of complete finite measure spaces and locally convex spaces in this work we present here new formulae for this e subdifferential under the presence of continuity type qualification conditions relying on the data involved in the integrand

randomization distributions and saddlepoint approximations in generalized linear models various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models these conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate examples include multinominal and dirichlet bootstraps the jackknife and permutation distributions the double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut

finding maximum likelihood estimates of patterned covariance matrices by the em algorithm some patterned covariance matrices used to model multivariate normal data that do not have explicit maximum likelihood estimates can be viewed as submatrices of larger patterned covariance matrices that do have explicit maximum likelihood estimates in such cases the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables the advantage of this perspective is that the em algorithm can be used to calculate the desired maximum likelihood estimates for the original problem two examples are presented

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

the foundations of finite sample estimation in stochastic processes generally in the literature on stochastic processes estimation is investigated in terms of asymptotic properties in this paper we establish some finite sample optimal estimation let y1 y2 be a discrete stochastic process since we will be discussing results for samples of finite size n we restrict the process to r in the following the term parameter is used in the same broad sense as by godambe thompson 1984 let y be a class of probability distributions f on r and 0 0 f f e jz be a real parameter let hi be a real function of y 1 yi and 0 be such that

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

the isserlis matrix and its application to non decomposable graphical gaussian models the operations of matrix completion and isserlis matrix construction arise in the statistical analysis of graphical gaussian models in both the bayesian and frequentist approaches in this paper we study the properties of the isserlis matrix of the completion of a positive definite matrix and propose an edge set indexing notation which highlights the symmetry existing between and its isserlis matrix in this way well known properties of can be exploited to give an easy proof of certain asymptotic results for decomposable graphical gaussian models as well as to extend such results to the non decomposable case in particular we consider the asymptotic variance of maximum likelihood estimators the non informative jeffreys prior the laplace approximation to the bayes factor the asymptotic distribution of the maximum likelihood estimators and the asymptotic posterior distribution of the parameters in a bayesian conjugate analysis in dealing with distributions over non decomposable models an extension of the hyper markov property to models with non chordal graphs is required our proposed extension is justified by an analysis of the conditional independence structure of the sufficient statistic

ignorable and informative designs in survey sampling inference summary the role of the sample selection mechanism in a model based approach to finite population inference is examined when the data analyst has only partial information on the sample design then a design which is ignorable when known fully may become informative conditions under which partially known designs can be ignored are established and examined for some standard designs the results are illustrated by an example used by scott 1977

adjustments to profile likelihood summary conditional and marginal likelihoods constructed from parameter dependent functions of the data have an additional parameter dependence that changes with the choice of supporting metric for the corresponding densities we consider constructing marginal and conditional likelihoods by using densities expressed in terms of an intrinsic choice of support measure based on either euclidean metric or the constant information metric barndorff nielsen s 1983 approximation to the distribution of the maximum likelihood estimate is used to approximate these conditional and marginal likelihoods the resulting likelihoods are closely related to the modified profile likelihood of barndorff nielsen 1983 and the approximate conditional likelihood of cox reid 1987 the normal circle problem is examined in some detail

on the bootstrap saddlepoint approximations we compare saddlepoint approximations to the exact distributions of a studentized mean and to its bootstrap approximation we show that on bounded sets these empirical saddlepoint approximations achieve second order relative errors uniformly we also consider the relative errors for larger deviations it follows that the studentized t bootstrap p value and the coverage of the bootstrap confidence interval have second order relative errors

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

reflection from a one dimensional totally refracting random multilayer ii internal field statistics the modeling of acoustic scattering by ocean sediments has led to the formulation of an idealized one dimensional problem involving the interplay of random scattering and total internal reflection the behavior of the reflection coefficient in the lossless case was discussed in w e kohler reflection from a one dimensional totally refracting multilayer siam j appl math 46 1986 pp 464 482 using the ideas of invariant embedding expressions for the mean field intensities and intensity fluctuations as functions of depth within the sediment layer are now derived

integration of subdifferentials of nonconvex functions in nonsmooth analysis and optimization subgradients come in many different flavors e g approximate dini proximal clarke generalized see 2 5 6 12 14 191 these subgradients are important and valuable tools however many questions remain unsolved concerning the exact link between the function and its subgradients for instance can two functions not differing by an additive constant have the same subgradients in this paper we study the fundamental problem of determining functions that can be recovered up to an additive constant from the knowledge of their subgradients this integration problem is not very well understood and very few functions or classes of functions are known to be recoverable from their subgradients in section 4 we show that if the basic constraint qualification holds at r then the composition of a closed i e lowersemicontinuous proper convex function with a twice continuously differentiable mapping is determined up to an additive constant by its generalized subgradients actually in this case all above mentioned subgradients are the same beside the obvious theoretical interest of this integration problem it is our hope or perhaps our long term goal that once this problem is better understood we can then tackle the question of uniqueness of solutions to generalized differential equations involving subgradients in place of partial derivatives an example of such an equation that well deserves study is the extended hamilton jacobi equation used in optimal control see clarke 2 let us also mention that a problem similar to the integration problem is the one of determining the set valued mappings that are in fact subgradient set valued mappings uniqueness is not mandatory for a contribution to this problem see janin 8 before we look at some of the known cases where the function can be recovered from its subgradients let us look at some negative examples it is clear that not every function can be recovered up to an additive constant from its subgradients we only need to look at the following two functions 0 x50 0 x10 f x 1 x o g x 2 x o

integration of subdifferentials of lower semicontinuous functions on banach spaces abstract this paper studies the lower semicontinuous functions on banach spaces whose subdifferentials are not disassociated from several conditions are given to ensure that two lower semicontinuous functions with the same subdifferential are equal up to an additive constant

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

saddlepoint approximations for distributions of quadratic forms in normal variables reference stat article 1999 001doi 10 1093 biomet 86 4 929view record in web of science record created on 2006 04 21 modified on 2017 05 12

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

local ancillarity in the presence of a nuisance parameter summary approximate ancillarity in the presence of a nuisance parameter is considered a theory of approximate s ancillarity based on the concept of local ancillarity introduced by cox 1980 is developed first and second order local s ancillarity are considered in detail and these results are applied to several examples these examples indicate that although first order local s ancillarity is a weak condition second order local s ancillarity is too strong a requirement for general use hence a second aspect of the paper is a study of the properties of an approximately ancillary statistic that are desirable for inference in the presence of a nuisance parameter this leads to a weaker definition of local ancillarity in the presence of a nuisance parameter that is satisfied in many cases

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

bayesian object identification this paper addresses the task of locating and identifying an unknown number of objects of different types in an image baddeley van lieshout 1993 advocate marked point processes as object priors whereas grenander miller 1994 use deformable template models in this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types using reversible jump markov chain monte carlo methods for inference green 1995 the naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this the first two expand the model space by introducing an additional unknown object type and the idea of a variable resolution template the third strategy utilising the first two augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects

a general framework for model based statistics summary this paper presents a general framework for model based statistics the framework is based on extended concepts of sufficiency and ancillarity the fundamental theorem of the new theory exhibits in a single equation the reference distributions for decision theory model checking and conditional inference for a general statistical model the theorem includes the equations upon which bayesian and frequentist statistics are founded the general theory also fills two gaps previously missing from empirical bayesian statistics concepts of sufficiency and conditional inference section 2 discusses a simple example in depth this example is just complicated enough to illustrate most of the new ideas it allows comparison of the new concepts with those already in the literature because it is so simple essential principles are emphasized section 3 describes the general framework extended concepts of sufficiency and ancillarity form the basis for the framework these extended concepts culminate in a simple but fundamental theorem the generality of the framework is illustrated throughout this section in particular frequentist bayesian robust bayesian empirical bayesian and prediction models are discussed the common framework emphasizes the similarities among various schools of statistical thought in fact besides varying interpreta tions of probability the only essential difference between schools is in the model itself section 4 derives new conditional empirical bayesian results for stein s estimator the estimated conditional mean squared error is shown to equal the posterior mean squared error with respect to the hyperprior that gives rise to stein s estimator section 5 discusses several more complicated empirical bayesian models some sugges tions are offered but for the most part the primary purpose of this section is to indicate the difficulties that must be faced for these problems section 6 offers concluding remarks these remarks summarize the advantages of the general framework

efficient conditional tests for mixture experiments with applications to the birth and branching processes summary conditional tests which are efficient in the sense of being uniformly most powerful unbiased for any sample size and are also asymptotically efficient with reference to a relevant likelihood in the sense of maximizing asymptotic power at alternatives converging to the null hypothesis are derived for mixture experiments involving dependent observations as simple applications efficient tests in birth processes branching processes stable additive processes etc are derived

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

subdifferential of the closed convex hull of a function and integration with nonconvex data in general normed spaces in this paper we approach the study of the subdifferential of the closed convex hull of a function and the related integration problem without the usual assumption of epi pointedness the key tool is as in hiriart urruty et al 2011 7 the concept of e subdifferential some other assumptions which are standard in the literature are also removed

integration of fenchel subdifferentials of epi pointed functions it is shown that in finite dimensions rockafellar s technique of integrating cyclically monotone operators applied to the fenchel subdifferential of an epi pointed function yields the closed convex hull of that function

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

model checking with nonparametric curves summary the use of local likelihood curve estimates in model checking is described test statistics are based on deviance differences and are interpreted using nonparametric bootstrap monte carlo some theoretical aspects are discussed methods are illustrated for regression with discrete data

integration formulas via the fenchel subdifferential of nonconvex functions abstract starting from explicit expressions for the subdifferential of the conjugate function we establish in the banach space setting some integration results for the so called epi pointed functions these results use the e subdifferential and the fenchel subdifferential of an appropriate weak lower semicontinuous lsc envelope of the initial function we apply these integration results to the construction of the lsc convex envelope either in terms of the e subdifferential of the nominal function or of the subdifferential of its weak lsc envelope

rao score tests for goodness of fit and independence summary rao s score statistic is a standard tool for carrying out hypothesis tests a unified approach is given which encompasses many common tests when a suitable group structure is present it is shown how the derivation of the test statistic can be simplified an omnibus test of multivariate normality is derived as an example of group invariance as another application of rao score tests a general method is given for constructing tests of independence

on bartlett adjustments for approximate bayesian inference summary in wide generality the posterior distributions of the likelihood ratio statistic and the posterior ratio statistic are chi squared to error of order o n where n is sample size the error in the chi squared approximation can be reduced to order o n 2 by bartlett correction in this paper explicit formulae are derived for the bartlett adjustment factors of both statistics and the derivations are based on the tierney kass kadane 1989 asymptotic approximation for marginal posterior probability density functions the use of numerical differentiation to facilitate calculation of the bartlett adjustments is also described some applications are considered that concern inference about regression models from both complete and right censored data

geometrical theory of higher order asymptotics of test interval estimator and conditional inference higher order asymptotic powers of one sided and two sided tests both conditional and unconditional are evaluated for a one parameter curved exponential family of distributions by using differential geometrical notions higher order asymptotic powers and the expected size of one sided and two sided interval estimators both conditional and unconditional are also obtained the tests and interval estimators which are third order most powerful at any arbitrary specified one point are explicitly designed with the help of the approximate ancillary statistic the characteristics of the conditional inference are elucidated by proving the equivalence up to the third order of the conditional inference and likelihood ratio inference geometrical notions such as curvatures and angles play a fundamental role in the present theory

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

stochastic turning point problem in a one dimensional refractive random multilayer a one dimensional model of random scattering is considered for a totally refracting random multilayer that has two separated spatial scales i e deterministic macroscale and random microscale the interplay of internal refraction and random multiple scattering for a turning point problem is analyzed with an intermediate scale of the wavelength two extended limit theorems for stochastic differential equations with a small parameter provide the characterization of the diffusion processes above and below the turning point both results are combined and a global limit law for the phenomenon of the random phase is obtained

the maximal normal operator space and integration of subdifferentials on nonconvex functions on definit des operateurs normaux maximaux et des fonctions primales sur des ensembles normaux on trouve que la normalite maximale est conservee dans plusieurs operations et que les operateurs normaux maximaux ont de bonnes proprietes de fermeture et de limitation

predictive fit for natural exponential families summary the paper examines predictive distributions concentrating on measuring their fit to the true distribution by average kullback leibler divergence the notion of an averaged bootstrap predictive distribution is introduced this predictive distribution is shown to be asymptotically superior to the estimative distribution in terms of average kullbackleibler divergence when the true distribution is in a natural exponential family smallsample results are presented for the poisson and binomial distributions which suggest that the bootstrap distribution performs well in these cases

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

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

an asymptotic diffusion limit for electromagnetic wave reflection from a random medium we consider a temporally pulsed electromagnetic wave obliquely incident upon a weakly dispersive and dissipative random multilayer the incident pulse width is chosen to be intermediate to two spatial scales with a deterministic macroscale and a random microscale an asymptotic diffusion limit theory of stochastic differential equations is extended to a noncentered system and applied to analyze the asymptotic interplay of random scattering and total internal reflection the perturbation analysis of the kolmogorov fokker planck equation is performed for the random reflection coefficient and the pseudodifferential operator theory is used to represent the transition probability density of it

a simple general formula for tail probabilities for frequentist and bayesian inference summary we describe a simple general formula for approximating the p value for testing a scalar parameter in the presence of nuisance parameters the formula covers both frequentist and bayesian contexts and does not require explicit nuisance parameterisation implementation is discussed in terms of computer algebra packages examples are given and the relationship to barndorff nielsen s approximation is discussed

on goodness of fit tests for the two parameter weibull distribution derived from the stabilized probability plot summary michael s statistic dsp based on the stabilized probability plot is considered for the assessment of goodness of fit of a two parameter weibull distribution this statistic is shown to have high power when the parameters are estimated using a procedure due to blom 1958 the correlation coefficient of the stabilized plot rsp is also proposed as a test statistic for this situation finally a family of transformations is obtained to reduce the null distribution of rsp to standard normality

the schwarz criterion and related methods for normal linear models in this paper we derive schwarz s information criterion and two modifications for choosing fixed effects in normal linear mixed models the first modification allows an arbitrary possibly informative prior for the parameter of interest replacing this prior with the normal unit information prior of kass wasserman 1995 and the generalised cauchy prior of jeffreys 1961 yields the usual schwarz criterion and a second modification respectively under the null hypothesis these criteria approximate bayes factors using the corresponding priors to increased accuracy in regression the second modification also corresponds asymptotically to the bayes factors of zellner siow 1980 and o hagan 1995 and is similar to the bayes factor of berger pericchi 1996 in mixed models the effective sample size term in schwarz s formula is ambiguous because of correlation between observations we propose an appropriate generalisation of schwarz s approximation and apply our results to evaluate a large class of models for repeated neuron area measurements in alcoholic and suicidal patients

model choice in generalised linear models a bayesian approach via kullback leibler projections summary we propose a general bayesian method of comparing models the approach is based on the kullback leibler distance between two families of models one nested within the other for each parameter value of a full model we compute the projection of the model to the restricted parameter space and the corresponding minimum distance from the posterior distribution of the minimum distance we can judge whether or not a more parsimonious model is appropriate we show how the projection method can be implemented for generalised linear model selection and we propose some markov chain monte carlo algorithms for its practical implementation in less tractable cases we illustrate the method with examples

a bayesian cart algorithm a stochastic search form of classification and regression tree cart analysis breiman et al 1984 is proposed motivated by a bayesian model an approximation to a probability distribution over the space of possible trees is explored using reversible jump markov chain monte carlo methods green 1995

on the relationship between empirical likelihood and empirical saddlepoint approximation for multivariate m estimators by comparing the expansions of the empirical log likelihood ratio and the empirical cumulant generating function calculated at the saddlepoint we investigate the relationship between empirical likelihood and empirical saddlepoint approximations this leads to a nonparametric approximation of the density of a multivariate m estimator based on the empirical likelihood and on the other hand it provides nonparametric confidence regions based on the empirical cumulant generating function some examples illustrate the use of the empirical likelihood in saddlepoint approximations and vice versa

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

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

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

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

on two families of transformations to additivity for binary response data summary two families of power transformations for probabilities are introduced to model symmetric and asymmetric departures from the logistic model the aim is to provide in a comprehensive way a representation of alternative scales in terms of which to carry out the analysis of binary response data maximum likelihood methods are employed to estimate an appropriate transformation using glim tests for detection of symmetric and asymmetric departures are proposed

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

quasi likelihood regression models with missing covariates summary this paper presents methods to handle missing covariates when the quasi likelihood equations for the complete data are available our suggestion is to replace the functions of the missing data appearing in the quasi likelihood equation with their conditional means given the observed data or with unbiased predictors so that the resulting equation is unbiased we focus on two models one is a random effects model for count data where random effects are treated as missing covariates the other is the overdispersed binomial regression model with partially missing covariates we also investigate the efficiency of the proposed estimates relative to the maximum likelihood estimators

on the unbiasedness of the papadakis estimator and other nonlinear estimators of treatment contrasts in field plot experiments summary spatial methods for the analysis of field plot experiments are considered estimators of treatment contrasts obtained by these methods are generally complicated nonlinear functions of the observations sufficient conditions for these estimators to be unbiased under a postulated true model are obtained the analysis of data from field plot experiments or other spatial experiments generally includes the estimation of treatment contrasts a common approach to their estimation is to apply ordinary least squares to a linear model in which the expected value of each observation is taken to be the sum of an overall mean a treatment effect and various environmental effects such as block or row and column effects this approach yields estimators which are linear functions of the observations and which are unbiased if the assumed model is correct recently numerous spatial methods for the analysis of data from field plot experi ments have been proposed see for example bartlett 1978 wilkinson et al 1983 besag kempton 1986 williams 1986 and gleeson cullis 1987 these alternatives to a traditional least squares analysis attempt to neutralize the disruptive effect that the spatial heterogeneity of the experimental units can have on the estimation of treatment contrasts randomization studies of uniformity trial data conducted by besag kempton 1986 indicate that spatial methods yield estimators of treatments contrasts which in the presence of appreciable spatial heterogeneity are likely to be more efficient than traditional estimators however because the estimators produced by spatial methods are complicated nonlinear functions of the observations little else is known about their properties in what follows we give conditions under which these estimators are unbiased under a postulated true model

on brondsted rockafellar s theorem for convex lower semicontinuous epi pointed functions in locally convex spaces in this work we give an extension of the brondsted rockafellar theorem and some of its important consequences to proper convex lower semicontinuous epi pointed functions defined in locally convex spaces we use a new approach based on a simple variational principle which also allows recovering the classical results in a natural way

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

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

multiparameter testing in exponential models third order approximations from likelihood summary for composite testing of several canonical components in an exponential model a conical or directional test provides a one dimensional measure of departure we approximate the distribution of this test statistic to third order by numerical inversion of a profile likelihood the method extends the lugannani rice type formula to kernels other than the normal

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

sequential monte carlo p values summary the assessment of statistical significance by monte carlo simulation may be costly in computer time this paper looks at a number of ways of calculating exact monte carlo p values by sequential sampling such p values are shown to have properties similar to those obtained by sampling with a fixed sample size both standard and generalized monte carlo procedures are discussed and in particular a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a markov chain conditioned to pass through the observed data

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