leverage local influence and curvature in nonlinear regression summary the connections between measures of leverage statistical curvature and the local influence of a mean shift perturbation are explored in nonlinear regression models the circumstances under which the jacobian leverage reduces to a commonly used linear approximation are found to be connected to the effective residual curvature of the nonlinear model the local influence of a mean shift perturbation in the model function is seen to be closely related to the jacobian leverage

multiple influential point detection in high dimensional regression spaces influence diagnosis should be routinely conducted when one aims to construct a regression model despite its importance the problem of influence quantification is severely under investigated in a high dimensional setting mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures although some progress has been made in recent years existing approaches are ineffective in detecting multiple influential points especially due to the notorious masking and swamping effects to address this challenge we propose a new group deletion procedure referred to as mip by introducing two novel quantities named max and min statistics these two statistics have complimentary properties in that the max statistic is effective for overcoming the masking effect while the min statistic is useful for overcoming the swamping effect combining their strengths we further propose an efficient algorithm that can detect influential points with prespecified guarantees for wider applications we focus on developing the new proposal for the multiple response regression model encompassing the univariate response linear model as a special case the proposed influential point detection procedure is simple to implement efficient to run and enjoys attractive theoretical properties its effectiveness is verified empirically via extensive simulation study and data analysis

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

local influence analysis of nonlinear structural equation models by regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete data log likelihood function in the em algorithm we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model the basic building blocks of local influence analysis are computed via observations of the latent variables generated by the metropolis hastings algorithm while the diagnostic measures are obtained via the conformal normal curvature seven perturbation schemes including some perturbation schemes on latent vectors are investigated the proposed procedure is illustrated by a simulation study and a real example

perturbation selection and local influence analysis for nonlinear structural equation model local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs one of its important issues is related to the appropriate choice of a perturbation vector in this paper we develop a general method to select an appropriate perturbation vector and a second order local influence measure to address this issue in the context of latent variable models an application to nonlinear structural equation models is considered six perturbation schemes are investigated including three schemes under which simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the influential ones the proposed procedure is illustrated by artificial examples and a simulation study as well as a real example

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

saddlepoint expansions for directional test probabilities an expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value in particular if the score function of a statistical model is chosen as this variable such a conditional probability gives a test for a simple hypothesis which is asymptotically equivalent to the likelihood ratio test the expansion is of the large deviation type and is derived through the use of saddlepoint methods thus the relative error of the test probability is o n1 uniformly in a bounded set for an average of n independent replications the approximation is based on the cumulant transform for the random variable but is otherwise a simple expression in terms of chi squared distributions in the one dimensional case it reduces to the expansion obtained by lugannani and rice numerical examples show an excellent fit comparable with other saddlepoint expansions when the dimension is low even for very small sample sizes but for higher dimensions more replications are required to give a similar approximation

estimating functions and approximate conditional likelihood summary the approximate conditional likelihood method proposed by cox reid 1987 is applied to the estimation of a scalar parameter 0 in the presence of nuisance parameters the estimating function of 0 based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood a sufficient condition for both approaches to be equivalent is given the role of parameter orthogonality is emphasized several examples including bivariate normal means with known coefficient of variation are presented

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

a unified proof on the weak hilbert 16th problem for n 2 abstract the weak hilbert 16th problem for n 2 was solved by horozov and iliev proc london math soc 69 1994 198 244 zhang and li adv in math 26 1997 445 460 gavrilov invent math 143 2001 449 497 and li and zhang nonlinearity 15 2002 1775 1992 by using different methods for different cases the aim of this paper is to give a unified and easier proof for all cases the proof is restricted to the real domain combines geometric and analytical methods and uses deformation arguments

on the choice of prior distribution for the box cox transformed linear model summary the noninformative prior distribution for the parameters of the linear model transformed following box cox 1964 has the non bayesian property of depending to some extent on the data an alternative choice of prior which is not outcome dependent was suggested by pericchi 1981 but it is argued here that this prior has some undesirable features an alternative family of non outcome dependent priors is suggested leading to a noninformative prior which is closer in spirit to that proposed by box cox the posterior consequences of adopting this prior are fully explored and an example discussed

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

a note on local influence based on normal curvature summary object functions other than the likelihood displacement such as a parameter estimate or a test statistic can also be used in local influence analysis the normal curvatures of these object functions have been studied in situations where the slopes were non zero in these situations we show that the normal curvature is not scale invariant and thus ambiguous conclusions will be drawn comments on the application of the general normal curvature formula are presented

local influence for incomplete data models this paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data the idea is to utilize cook s approach to the conditional expectation of the complete data log likelihood function in the em algorithm it is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods an application to the generalized linear mixed model is investigated some illustrative artificial and real examples are presented

case deletion diagnostics for linear mixed models based on the q function the conditional expectation of the logarithm of the joint likelihood between responses and random effects we propose a case deletion approach to identify influential subjects and influential observations in linear mixed models the models considered here are very broad in the sense that any covariance structures can be specified in the covariance matrices of the random effects and random errors analytically explicit forms of diagnostic measures for the fixed effects and variance components are provided comparisons with existing methods including likelihood based case deletion and local influence methods are made numerical results including real data analysis and simulation studies are presented for both illustration and comparison this article has supplementary material online

a simple predictive density function abstract an easily computable predictive density is considered although involving a plain maximum likelihood technique it coincides with the posterior predictive density with a noninformative prior for standard situations achievements are comparable with classical inference

the cyclicity of period annuli for a class of cubic hamiltonian systems with nilpotent singular points abstract this paper deals with the limit cycles of a class of cubic hamiltonian systems under polynomial perturbations we suppose that the corresponding hamiltonian system which has at least one center has finite singular points and is symmetrical with respect to both x axis and y axis and also the origin is a nilpotent singular point hence the hamiltonian h x y can be written as h x y x 2 a x 4 b x 2 y 2 c y 4 a b c r 3 c 0 for the above h x y the corresponding vector field is x 2 y b x 2 2 c y 2 y 2 x 1 2 a x 2 b y 2 we first obtain that the above vector fields with at least one center can be divided into 8 classes by its topological phase portraits for the following perturbed system x 2 y b x 2 2 c y 2 e f x y y 2 x 1 2 a x 2 b y 2 e g x y where 0 e 1 f x y and g x y are polynomials in x y with degree n we give an estimation of the number of isolated zeros of the corresponding abelian integral the number of limit cycles follows from poincare pontryagin theorem

conformal normal curvature and assessment of local influence in 1986 r d cook proposed differential geometry to assess local influence of minor perturbations of statistical models we construct a conformally invariant curvature the conformal normal curvature for the same purpose this curvature provides a measure of local influence ranging from 0 to 1 with objective bench marks to judge largeness we study various approaches to using the conformal normal curvature and the relationships between these approaches

bayesian sensitivity analysis with the fisher rao metric we propose a geometric framework to assess sensitivity of bayesian procedures to modelling assumptions based on the nonparametric fisher rao metric while the framework is general the focus of this article is on assessing local and global robustness in bayesian procedures with respect to perturbations of the likelihood and prior and on the identification of influential observations the approach is based on a square root representation of densities which enables analytical computation of geodesic paths and distances facilitating the definition of naturally calibrated local and global discrepancy measures an important feature of our approach is the definition of a geometric contamination class of sampling distributions and priors via intrinsic analysis on the space of probability density functions we demonstrate the applicability of our framework to generalized mixed effects models and to directional and shape data

bayesian influence analysis a geometric approach in this paper we develop a general framework of bayesian influence analysis for assessing various perturbation schemes to the data the prior and the sampling distribution for a class of statistical models we introduce a perturbation model to characterize these various perturbation schemes we develop a geometric framework called the bayesian perturbation manifold and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model we develop intrinsic influence measures and local influence measures based on the bayesian perturbation manifold to quantify the effect of various perturbations to statistical models theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal bayesian analysis

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

consistent estimation of limited dependent variable models despite misspecification of distribution abstract by exploiting conditions on the behavior of regressors estimators are developed which are consistent up to a factor of proportionality for the slope coefficients of the regression function of a imperfectly observed dependent variable limited dependent variables are a special case of interest the consistency is robust to misspecification of the distribution of the latent dependent variable the estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

local influence to detect influential data structures for generalized linear mixed models biometrics 2001 dec 57 4 1166 72 related articles books linkout local influence to detect influential data structures for generalized linear mixed models ouwens mj tan fe berger mp department of methodology and statistics maastricht university the netherlands mario ouwens stat unimaas nl this article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects for these models it is shown that the subject oriented influence measure is a special case of the proposed observation oriented influence measure a two step diagnostic procedure is proposed the first step is to search for influential subjects a search for influential observations is proposed as the second step an illustration of a two treatment multiple period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

analysis of infant growth curves using multivariate adaptive splines summary in this paper we study the effect of cocaine use by a pregnant woman on the growth of her infant after birth using a data set from a retrospective study we found that cocaine use was a marginally significant contributor to the infant growth as measured by bodyweight prom a statistical point of view the data represent a common though complex structure that has received little attention in the statistical literature to analyze these data we adopt and further enhance an approach developed recently called masal multivariate adaptive splines for the analysis of longitudinal data in addition to the fitting of growth curves we demonstrate particularly how to explore and estimate the underlying covariance structures for the longitudinal data that were collected from a rather irregular schedule

linear estimate of the number of zeros of abelian integrals for a kind of quartic hamiltonians abstract an upper bound b n 7n 5 is derived for the number of zeros of abelian integrals i h h g x y dy f x y dx on the open interval where h is an oval lying on the algebraic curve h x y 1 2 y2 u x h deg u x 4 and is the maximal interval of existence of h f x y g x y are polynomials of x and y and n max deg f x y deg g x y

buchsbaum rim multiplicities as hilbert samuel multiplicities abstract we study the buchsbaum rim multiplicity br m of a finitely generated module m over a regular local ring r of dimension 2 with maximal ideal m the module m under consideration is of finite colength in a free r module f write f m i j where j i are m primary ideals of r we first investigate the colength l r a of any m primary ideal a and its hilbert samuel multiplicity e a using linkage theory as an application we establish several multiplicity formulas that express the buchsbaum rim multiplicity of the module m in terms of the hilbert samuel multiplicities of ideals related to i j and a minimal reduction of m the motivation comes from work by e jones who applied graphical computations of the hilbert samuel multiplicity to the buchsbaum rim multiplicity e jones computations of buchsbaum rim multiplicities j pure appl algebra 162 2001 37 52

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

approximate inference in location scale regression models abstract it is shown that 2 and multivariate t distributions provide good approximations to posterior distributions arising in location scale regression models in the case of a linear regression model bayesian inferences based on an improper prior have conditional frequency as well as fiducial structural interpretation so the results are also applicable in a non bayesian context numerical support for the approximations is presented for the case of a weibull regression model and a regression with t distributed errors

the score statistic for regression transformation summary the score statistic for regression transformation using a parametric family is developedfurther a simple formula for the approximate variance matrix of score statistics basedon asymptotic theory is applied to yield the score statistic t s for regression transforma tion this is compared to atkinson s t d statistic for the same problem and yields animprovement to its standardization simulations indicate that the significance levels ofthe proposed score statistic t s are very close to their nominal values some key words power transformation regression score statistic simulation tests for normality 1 introduction the work of box cox 1964 has been the basis of many investigations into theuse of transformations in regression analysis and the current state of the topic is wellsummarized in the monographs of cook weisberg 1982 and atkinson 1985 theprincipal aim of the original work was to transform a response or dependent variable sothat it would satisfy the normality and other standard assumptions of regression analysis the authors used a parametric family of transformations to achieve this and placedemphasis on estimating its parameters in subsequent work andrews 1971 was moreconcerned with testing transformation parameters while atkinson 1973 introducedanother statistic for this purpose from consideration of both andrews s statistic and scoreor c a tests the present paper develops a standardized score statistic in the case of ascalar transformation parameter in effect it is found to provide the standardization ofatkinson s statistic an aspect which atkinson 1973 believed to be theoretically intract able and avoided by using an approximate regression argument

regression transformation diagnostics using local influence abstract following box and cox 1964 the use of transformations in regression analysis is now common recently there has been emphasis on diagnostic methods for transformation much of which has involved deletion of data cases summaries were given by cook and weisberg 1982 and atkinson 1985 this article obtains diagnostics for the estimated regression parameter of the box cox transformation of the response variable in the linear model instead of deleting cases the more general notions of perturbing assumptions of the model or components of the data are employed as in the local influence approach of cook 1986 the diagnostics then arise from local changes to the transformation parameter estimate caused by small perturbations the case direction in which small perturbations have the greatest effect is the main diagnostic quantity an appeal of the approach is that it allows simultaneous perturbations affecting all data cases not just one at a time deletions it can thus point to groups of in

length formulas for the local cohomology of exterior powers in 10 huneke noted a proof due to hochster of the following theorem of angeniol and giusti see 1 let r be a local ring n m and g r r a homomorphism such that grade im g n m l suppose the cokernel n of g has finite length then this length equals the length of r ira g n 2 r ira g by i g we denote the ideal in r generated by the m x m minors of a matrix representing g it is well known see 7 that n m 1 is the maximal possible grade if im g t r therefore r is a cohen macaulay ring of dimension n m 1 we further notice that angeniol and giusti in addition assume r to contain the rational numbers and that the theorem has been known for a long time if m n 9 21 10 17 2 in this paper we shall study the problem of angeniol and giusti in a more general context we start from the dual situation f rm r being a homomorphism which we assume to be injective this is equivalent to grade ira f 1 given a basis x of r m and an orientation 7 on r i e an

transformation model diagnostics we apply the local influence method of lawrance to assess the effect of the case weights perturbation on the transformation power estimator in the box cox regression model we show that this method is the same as the local influence method proposed by cook furthermore the difference in local influence diagnostics between the case weights perturbation and the constant variances perturbation is examined and the relationship between the localinfluence diagnostic and the deletion diagnostic is studied an example is presented to illustrate local influence diagnostics

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

the buchsbaum rim polynomial of a module abstract for a noetherian local ring r m the hilbert functions of m primary ideals provide considerable information about constructions and singularities coded by the ideal for a module e which is the analogue of such ideals e is a proper submodule of a free module so that the quotient has finite length buchsbaum and rim defined a similar function and introduced the notion of buchsbaum rim multiplicity br e of the module unlike in the ideal case the information about these functions is still scant when r is cohen macaulay of dimension d 1 and e has rank r we develop some of their properties sufficiently enough to establish the following bound for the reduction number of the module e r e d r 1 br e 2 1 the same techniques lead to bounds on the number of generators of the integral closure of the powers of certain ideals and modules

zeroes of complete elliptic integrals for 1 2 resonance abstract we give an estimate for the number of zeroes of the elliptic integral i h a x y dx b x y dy along the ovals h x y h h x y y 2 2 x 2 x 4 in terms of the degrees of the symmetric polynomials a and b

a bayesian approach to transformations to normality summary the analysis of transformation of observations in the linear model with normal errors proposed by box cox 1964 is considered a different choice of noninformative unnormed prior is advocated which is not outcome dependent this new selection of prior leads to a formal identity between likelihood and bayesian inference both for the estimation of the best transformation to normality and for the presence of homoscedasticity and additivity under this transformation extension to a related problem is mentioned

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

a diagnostic procedure based on local influence cook s 1986 normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models however there is no rigorous approach based on the normal curvature for addressing two fundamental issues to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated and to identify suspicious data points for which the discrepancy is most evident our purpose is to establish a theoretically sound procedure for resolving these issues for case weight perturbation under the framework of independent distributions we show that the local influence measure cook s distance and likelihood distance are asymptotically equivalent a diagnostic procedure based on local influence is proposed for evaluating model misspecification and for detecting influential points simultaneously we analyse two real datasets

differential geometry of curved exponential families curvatures and information loss the differential geometrical framework is given for analyzing statistical problems related to multi parameter families of distributions the dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint the duality connected by the legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures the second order information loss is calculated for fisher efficient estimators and is decomposed into the sum of two non negative terms one is related to the exponential curvature of the statistical model and the other is related to the mixture curvature of the estimator only the latter term depends on the estimator and vanishes for the maximum likelihood estimator a set of statistics which recover the second order information loss are given the second order efficiency also is obtained the differential geometry of the function space of distributions is discussed

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

second order approach to local influence to examine global and local influence and their relations for regression models we study the perturbation formed surface of a variable such as the maximum likelihood estimate of a parameter by evaluating the second derivative or curvature of the surface the corresponding slope of this surface is related to the curvature of the likelihood displacement surface of cook examples show that this approach with the aid of plots is helpful not only to discover influential cases including those hidden in an individual global sense but also to understand the nature of influence

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

on the number of zeros of abelian integrals for a kind of quartic hamiltonians an explicit upper bound b n is derived for the number of zeros of abelian integrals i h email protected c hg x y dx f x y dy on the open interval 0 1 4 where c h is an oval lying on the algebraic curve h x y x 2 y 2 x 4 ax 2y 2 y 4 with a 2 f x y and g x y are polynomials in x and y of degrees not exceeding n assume i h not vanish identically then b n 3n 14 12n 34 23

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

constructing indecomposable integrally closed modules over a two dimensional regular local ring in this article we construct integrally closed modules of rank two over a two dimensional regular local ring the modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters then we investigate their indecomposability as a consequence we have a large class of indecomposable integrally closed modules whose fitting ideal is not simple this gives an answer to kodiyalam s question

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

local influence for generalized linear models with missing covariates in the analysis of missing data sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions in this article we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data we examine two types of perturbation schemes the single case and global perturbation schemes for perturbing various assumptions in this setting we show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation we also develop several local influence measures to identify influential points and test model misspecification simulation studies are conducted to evaluate our methods and real datasets are analyzed to illustrate the use of our local influence measures

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

estimate of the number of zeros of abelian integrals for a kind of quartic hamiltonians with two centers abstract in this paper we give the upper bound of the number of zeros of abelian integral i h h p x y d x q x y d y where h is the closed orbit defined by h x y x 2 x 4 y 4 h 0 h is the maximal open interval on which the ovals h exist p x y and q x y are real polynomials in x and y of degree at most n