modified signed log likelihood ratio summary the signed log likelihood ratio r for a one dimensional interest parameter can be modified as r r r log u r so that r is asymptotically standard normally distributed with error of order o n 3 2 u being interpretable as a test statistic a new more direct derivation of this result is given which leads to a more explicit expression for u and provides a better handle on the error term the relation of the tail area approximation determined by r to a generalization of the lugannani rice approximation is discussed and the applicability of r to the analysis of residual variation is indicated

stable and invariant adjusted directed likelihoods summary for the purpose of making inferences for a one dimensional interest parameter or constructing approximate complementary ancillaries or residuals the directed likelihood or signed square root of the likelihood ratio statistic can be adjusted so that the resulting modified directed likelihood is under ordinary repeated sampling approximately standard normal with error of o n 312 conditional on a suitable ancillary statistic and hence unconditionally in general suitable specification of the ancillary statistic may be difficult we introduce two adjusted directed likelihoods which are similar to the modified directed likelihood but do not require the specification of the ancillary statistic the error of the standard normal approximation to the distribution of these new adjusted directed likelihoods is o n 1 conditional on any reasonable ancillary statistic which is still an improvement over the unadjusted directed likelihoods

reml estimation asymptotic behavior and related topics the restricted maximum likelihood reml estimates of dispersion parameters variance components in a general non normal mixed model are defined as solutions of the reml equations in this paper we show the reml estimates are consistent if the model is asymptotically identifiable and infinitely informative under the location invariant class and are asymptotically normal a n if in addition the model is asymptotically nondegenerate the result does not require normality or boundedness of the rank p of design matrix of fixed effects moreover we give a necessary and sufficient condition for asymptotic normality of gaussian maximum likelihood estimates mle in non normal cases as an application we show for all unconfounded balanced mixed models of the analysis of variance the reml anova estimates are consistent and are also a n provided the models are nondegenerate the mle are consistent a n if and only if certain constraints on p are satisfied

optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps abstract in this paper the optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps is considered we introduce two kinds of environmental perturbations in this model one is called white noise which is continuous and is described by a stochastic integral with respect to the standard brownian motion and the other one is jumping noise which is modeled by a levy process under some mild assumptions the critical values between extinction and persistent in the mean of each species are established the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained we utilize the ergodic method to discuss the optimal harvesting problem the results show that white noises and levy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases at last some numerical examples are introduced to show the validity of our results

approximations for densities of sufficient estimators abstract a simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described it is an extension of the one developed by o barndorff nielsen and d r cox 1979 for exponential families a series expansion in powers of n 1 is derived of which the first term has an error of order n 1 which can effectively be reduced to n 3 2 by renormalization the results obtained are similar to those given by h e daniels s 1954 saddlepoint method but the derivations are simpler a brief treatment of approximations to conditional densities is given theorems are proved which extend the validity of the multivariate edgeworth expansion to parametric families of densities of statistics which need not be standardized sums of independent and identically distributed vectors these extensions permit the treatment of problems arising in time series analysis the technique is used by j durbin 1980 to obtain approximations to the densities of partial serial correlation coefficients

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

on the structure of transformation models in this paper we characterize transformation models by means of the functional form of the densities we discuss sufficiency of the pair t where t is an equivariant estimator and v is a maximal invariant furthermore we introduce and discuss the algebraic concept of structural sufficiency this gives rise to an example of a transformation model where t a is nonsufficient 1 introduction in the analysis of statistical models it is sometimes convenient to make use of invariance properties of the model in question for instance the invariance principle see lehmann 20 or hall wijsman and ghosh 16 is a widely accepted and frequently used statistical tool closely related to this concept is the notion of transformation models let e be a sample space e a parameter set and g a group acting on e and e in our setup a transformation model is a family of probability measures p 9 with the property

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

practical small sample asymptotics for regression problems abstract saddlepoint approximations are derived for sums of independent but not necessarily identically distributed random variables along with generalizations to estimating equations and multivariate problems these results are particularly useful for accurately approximating the distribution of regression coefficients general formulas are given for the distribution of the coefficients arising out of a generalized linear model with both canonical and noncanonical link functions we illustrate the case of logistic regression with a real data example and show how the gibbs sampler may be used to obtain confidence sets for each regression parameter based on the saddlepoint approximation

a note on the relation between modified profile likelihood and the cox reid adjusted profile likelihood summary an adjustment to the profile likelihood proposed by cox reid 1987 when the parameters are orthogonal is shown to agree with modified profile likelihood in a number of instances in which the parameters are not orthogonal several examples of the phenomenon are given in the case of composite transformation models with invariant parameter as the parameter of interest it is shown that the cox reid adjustment agrees with modified profile likelihood in a large deviation sense if lebesgue measure is rightinvariant necessary and sufficient conditions for equivalence in the moderate deviation sense of modified profile likelihood and the cox reid adjusted profile likelihood are

groups acting on gaussian graphical models gaussian graphical models have become a well recognized tool for the analysis of conditional independencies within a set of continuous random variables from an inferential point of view it is important to realize that they are composite exponential transformation families we reveal this structure by explicitly describing for any undirected graph the maximal matrix group acting on the space of concentration matrices in the model the continuous part of this group is captured by a poset naturally associated to the graph while automorphisms of the graph account for the discrete part of the group we compute the dimension of the space of orbits of this group on concentration matrices in terms of the combinatorics of the graph and for dimension zero we recover the characterization by letac and massam of models that are transformation families furthermore we describe the maximal invariant of this group on the sample space and we give a sharp lower bound on the sample size needed for the existence of equivariant estimators of the concentration matrix finally we address the issue of robustness of these estimators by computing upper bounds on finite sample breakdown points keywords gaussian graphical models covariance matrix concentration matrix robust estimator breakdown point equivariant estimator transformation families

approximate predictive pivots and densities summary this paper suggests two predictive likelihoods that can be applied in almost any parametric model setting the first can sometimes be interpreted as an approximate predictive pivot barnard 1986 while the second is often an approximation to a bayesian predictive density with a flat prior the issue of calibrating various predictive likelihoods in terms of long run predictive coverage is also discussed and a specific criterion by which these likelihoods can be compared is proposed

stability and instability of stationary solutions for sublinear parabolic equations abstract in the present paper we study the initial boundary value problem of the sublinear parabolic equation we prove the existence of solutions and investigate the stability and instability of stationary solutions we show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent we prove that small stationary solutions are unstable for one space dimensional autonomous equations we elucidate the structure of stationary solutions and study the stability of all stationary solutions

frequentist and bayesian bartlett correction of test statistics based on adjusted profile likelihoods summary for inference about a multidimensional parameter b in the presence of nuisance param

information bias and adjusted profile likelihoods summary the bias and information bias of the ordinary profile score statistic are both typically of order 0 1 several additive adjustments to the profile score statistic that reduce its bias to order o n have been proposed in certain situations the information bias of these adjusted profile score statistics is also reduced to order o n q specifically the modified profile likelihood of barndorff nielsen yields an adjusted profile score statistic having both reduced bias and reduced information bias in general however a bias reducing adjustment to the profile score statistic will not automatically reduce the order of the information bias as well in this paper an analytical formula is obtained for the information bias of a general bias adjusted profile score statistic this formula is used to compare bias reducing adjustments to the profile score statistic as well as to construct further adjustments that reduce the information bias to o n 1 several examples are presented to illustrate use of the formula for information bias in particular the information bias formula may be utilized in a criterion for choosing between orthogonal parameterizations for the conditional profile likelihood of cox and reid

on the equivalence of prospective and retrospective likelihood methods in case control studies summary we present new approaches to analyzing case control studies using prospective likelihood methods in the classical framework we extend the equality of the profile likelihoods to the barndorff nielsen modified profile likelihoods for prospective and retrospective models this enables simple and accurate approximate conditional inference for stratified case control studies of moderate stratum size in the bayesian framework we provide sufficient conditions on priors for the prospective model parameters to yield a prospective marginal posterior density equal to its retrospective counterpart our results extend the prospective retrospective equivalence in the bayesian paradigm with a more general class of priors than has previously been investigated

exponential transformation models the class of exponential transformation models i e transformation models that are also exponential families is investigated it is shown by using standard exponential family theory that the group of transformations on the sample space generating the model induces affine transformation groups on the parameter space and on the range space of the minimal sufficient statistic the induced groups being in fact representations of the original transformation group the model function may be explicitly expressed in terms of these representations and it possesses a number of important properties the possibility of extending exponential transformation models to larger composite exponential transformation models is considered such extensions serving for instance the purpose of model control the inference for composite exponential transformation models is described in general terms and examples of such models are discussed the paper starts with an introduction to transformation models and a unified treatment of their distribution theory required in the subsequent discussion of the exponential transformation models

efficiency of projected score methods in rectangular array asymptotics summary the paper considers a rectangular array asymptotic embedding for multistratum data sets in which both the number of strata and the number of within stratum replications increase and at the same rate it is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non zero mean in its asymptotic normal distribution by using a projection operator on the score function an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the cram6r rao lower bound the adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator

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

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