edgeworth correction by bootstrap in autoregressions we prove that the distribution of least squares estimates in autoregressions can be bootstrapped with accuracy o n 1 2 a s thereby improving the normal approximation error of o n

hellinger deviance tests efficiency breakdown points and examples abstract hellinger distance analogs of likelihood ratio tests are proposed for parametric inference the proposed tests are based on minimized hellinger distances between nonparametric density estimates and densities corresponding to null and unconstrained parametric models if the parametric model is correct the hellinger deviance test is asymptotically equivalent to the likelihood ratio test a simulation study examines the relative performance of these tests in finite samples breakdown properties of the hellinger deviance tests and likelihood ratio tests are compared the hellinger tests are generally high breakdown point tests whereas in many instances the likelihood ratio tests have breakdown points of 0 two numerical examples illustrate the implementation and performance of the proposed tests likelihood based methods are widely used in applications they provide a routine method for generating efficient estimates and inference statements in many instances however these methods are known to

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

least squares variogram fitting by spatial subsampling summary least squares methods are popular for fitting valid variogram models to spatial data the paper proposes a new least squares method based on spatial subsampling for variogram model fitting we show that the method proposed is statistically efficient among a class of least squares methods including the generalized least squares method further it is computationally much simpler than the generalized least squares method the method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation an extension of the method proposed to a class of spatial regression models is illustrated with a real data example results from a simulation study on finite sample properties of the method are also reported

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

a short proof of a theorem of m hashimoto abstract recently m hashimoto announced that the resolutions of determinantal ideals depend on the characteristic of the base field the purpose of this note is to give a short proof of this result one should stress that even though the method we use is different from hashimoto s his result provided us with the clue where the additional relation exists

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

homogeneity tests against central mixture alternatives abstract a test of homogeneity is derived for a general sampling model the alternative hypothesis is a mixture over a parameter of the sampling model centered at the null hypothesis the test statistic is derived through a score test its functional form is independent of the particular mixing distribution suppose yi i 1 n are independent random variables with respective probability density or mass functions fi yi i under the null hypothesis suppose all i homogeneous and equal to the common value 0 under the alternative hypothesis suppose the i behave as random samples taken from a distribution with mean 0 and finite third moment the score statistic for testing these hypotheses rejects the null for large values of where is the maximum likelihood estimate of 0 under the null hypothesis and when the sample size n is large s is normally distributed under both the null hypothesis and a sequence of alternative hypotheses in which the variance of the mixing distribution tends

on optimal spatial subsample size for variance estimation we consider the problem of determining the optimal block or subsample size for a spatial subsampling method for spatial processes observed on regular grids we derive expansions for the mean square error of the subsampling variance estimator which yields an expression for the theoretically optimal block size the optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets optimal block sizes are computed for sampling regions of a number of commonly encountered shapes numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size

unsupervised self normalized change point testing for time series abstractwe propose a new self normalized method for testing change points in the time series setting self normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean however it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series and its adaptation to change point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power compared with existing results on using self normalization in this direction the current article proposes a new self normalized change point test that does not require prespecifying the number of total change points and is thus unsupervised in addition we propose a new contrast based approach in generalizing self normalized statistics to handle quantities other than the mean which is specifically tailored for change point testing monte car

asymptotic expansions for sums of block variables under weak dependence let x i be a sequence of random vectors and y in f in x i l be zero mean block variables where x i l x i x i l 1 i 1 are overlapping blocks of length l and where f in are borel measurable functions this paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums n i 1 x i and n i 1 y in under weak dependence conditions on the sequence x i i when the block length t grows to infinity in contrast to the classical edgeworth expansion results where the terms in the expansions are given by powers of n 1 2 the expansions derived here are mixtures of two series one in powers of n 1 2 and the other in powers of n l 1 2 applications of the main results to i expansions for studentized statistics of time series data and ii second order correctness of the blocks of blocks bootstrap method are given

characteristic free representation theory of the general linear group on etudie systematiquement les z formes des representations rationnelles du groupe lineaire generale

asymptotic expansions for sums of weakly dependent random vectors it is shown that formal edgeworth expansions are valid for sums of weakly dependent random vectors the error of approximation has ordero n s 2 2 if the strong mixing coefficients in iii are decreasing at an exponential rate the above conditions can easily be checked and are often satisfied when the sequence of random vectors is a gaussian or a markov or an autoregressive process explicit formulas are given for the distribution of finite fourier transforms of a strictly stationary time series

on nonparametric variance estimation for second order statistics of inhomogeneous spatial point processes with a known parametric intensity form we introduce new variance estimation procedures for second order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes the statistics are defined either on a subset b of the observation window or on the whole window for the former we use subblocks that have the same size and shape as b as replicates of b in order to estimate the target variance for the latter we develop a subsampling estimator for a key component in the target variance and estimate its other components by method of moment methods under some suitable conditions we prove that the proposed variance estimators are consistent for the target variances in both cases simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods this article has supplementary material online

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

a note on overdispersed exponential families abstract the issue of creating overdispersion in a given one parameter one dimensional exponential family by extending it to a two parameter exponential family with the same support is considered an easily verifiable sufficient condition for this is derived it is shown that a large class of families satisfy this condition and that this class includes efron s 1986 and lindsay s 1986 family as special cases this class is also closely related to jorgensen s 1988 exponential dispersion models ump unbiased tests for testing overdispersion are exhibited and it is shown that in this context cox s overdispersion test is a special case a graphical display is developed to select a family of the general class which should be used with a given set of data to overdisperse a given target one parameter family two real data illustrations are given kr

second order correctness of the blockwise bootstrap for stationary observations we show that the blockwise bootstrap approximation for the distribution of a studentized statistic computed from dependent data is second order correct provided we choose an appropriate variance estimator we also show how to adapt the bc a confidence interval of efron to the dependent case for the proofs we extend the results of gotze and hipp on the validity of the formal edgeworth expansion for a sum to the studentized mean

minimum hellinger distance estimation for finite mixtures of poisson regression models and its applications il a ete montre que l estimation au minimum de la distance de hellinger mhde reduit des points irreguliers par effet de lissage avec une efficacite du premier ordre pour un modele correctement specifie on propose une approche d estimation adaptee aux melanges finis de modeles de regression de poisson basee sur la mhde les simulations de monte carlo montrent a l evidence que la mhde est une alternative viable a l estimation au maximum de vraisemblance lorsque les composants du melange ne sont pas bien separes ou lorsque les parametres du modele sont proches de zero des applications de biometrie illustrent egalement l utilite pratique de la methode mhde

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

practical identifiability of finite mixtures of multivariate bernoulli distributions the class of finite mixtures of multivariate bernoulli distributions is known to be nonidentifiable that is different values of the mixture parameters can correspond to exactly the same probability distribution in principle this would mean that sample estimates using this model would give rise to different interpretations we give empirical support to the fact that estimation of this class of mixtures can still produce meaningful results in practice thus lessening the importance of the identifiability problem we also show that the expectation maximization algorithm is guaranteed to converge to a proper maximum likelihood estimate owing to a property of the log likelihood surface experiments with synthetic data sets show that an original generating distribution can be estimated from a sample experiments with an electropalatography data set show important structure in the data

a general maximum likelihood analysis of variance components in generalized linear models this paper describes an em algorithm for nonparametric maximum likelihood ml estimation in generalized linear models with variance component structure the algorithm provides an alternative analysis to approximate mql and pql analyses mcgilchrist and aisbett 1991 biometrical journal 33 131 141 breslow and clayton 1993 journal of the american statistical association 88 9 25 mcgilchrist 1994 journal of the royal statistical society series b 56 61 69 goldstein 1995 multilevel statistical models and to gee analyses liang and zeger 1986 biometrika 73 13 22 the algorithm first given by hinde and wood 1987 in longitudinal data analysis 110 126 is a generalization of that for random effect models for overdispersion in generalized linear models described in aitkin 1996 statistics and computing 6 251 262 the algorithm is initially derived as a form of gaussian quadrature assuming a normal mixing distribution but with only slight variation it can be used for a completely unknown mixing distribution giving a straightforward method for the fully nonparametric ml estimation of this distribution this is of value because the ml estimates of the glm parameters can be sensitive to the specification of a parametric form for the mixing distribution the nonparametric analysis can be extended straightforwardly to general random parameter models with full npml estimation of the joint distribution of the random parameters this can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters a simple method is described for obtaining correct standard errors for parameter estimates when using the em algorithm several examples are discussed involving simple variance component and longitudinal models and small area estimation

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

moment estimation for statistics from marked point processes in spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations in other words the data form a realization of a marked point process in this paper we formulate subsampling estimators of the moments of general statistics computed from marked point process data and we establish their l 2 consistency the variance estimator in particular can be used for the construction of confidence intervals for estimated parameters a practical data based method for choosing a subsampling parameter is given and illustrated on a data set finite sample simulation examples are also presented

minimum hellinger distance estimation for the analysis of count data abstract minimum hellinger distance mhd estimation is studied in the context of discrete data the mhd estimator is shown to provide an effective treatment of anomalous data points and its properties are illustrated using short term mutagenicity test data asymptotic normality for a discrete distribution with countable support is derived under a readily verified condition on the model breakdown properties of the mhd estimator and an outlier screen are compared count data occur frequently in statistical applications for instance in chemical mutagenicity studies which comprise an important step in the identification of environmental carcinogens much of the resultant data are counts woodruff mason valencia and zimmering 1984 reported anomalous counts in the sex linked recessive lethal test in drosophila these outliers can have a substantial impact on the experimental conclusions mhd estimation provides a means for reliable inference when modeling count data that are prone to outliers the mh

weighted empirical adaptive variance estimators for correlated data regression estimating equations based on marginal generalized linear models are useful for regression modelling of correlated data but inference and testing require reliable estimates of standard errors we introduce a class of variance estimators based on the weighted empirical variance of the estimating functions and show that an adaptive choice of weights allows reliable estimation both asymptotically and by simulation in finite samples connections with previous bootstrap and jackknife methods are explored the effect of reliable variance estimation is illustrated in data on health effects of air pollution in king county washington

bootstrap confidence regions computed from autoregressions of arbitrary order summary given a linear time series e g an autoregression of infinite order we may construct a finite order approximation and use that as the basis for bootstrap confidence regions the sieve or autoregressive bootstrap as this method is often called is generally seen as a competitor with the better understood block bootstrap approach however in the present paper we argue that for linear time series the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities in particular since it does not corrupt second order properties then it may be used in a double bootstrap form with the second bootstrap application being employed to calibrate a basic percentile method confidence interval this approach confers secondorder accuracy without the need to estimate variance that offers substantial benefits since variances of statistics based on time series can be difficult to estimate reliably and partly because of the relatively small amount of information contained in a dependent process are notorious for causing problems when used to studentize other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter here equal to the autoregressive order and the fact that in contradistinction to the case of the block bootstrap the percentile t version of the sieve bootstrap may be based on the raw estimator of standard error in the process of establishing these properties we show that the sieve bootstrap is second order correct

sysygies of unimodular lawrence ideals infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra the quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal which defines a toric subvariety in a product of projective lines connections to graphic arrangements and to beilinson s spectral sequence are explored

minimum hellinger distance estimation for k component poisson mixture with random effects the k component poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations however the residual maximum likelihood estimation reml of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination in the literature the minimum hellinger distance mhd estimation has been investigated to obtain robust estimation for finite poisson mixtures this article aims to develop a robust mhd estimation approach for k component poisson mixtures with normally distributed random effects by applying the gaussian quadrature technique to approximate the integrals involved in the marginal distribution the marginal probability function of the k component poisson mixture with random effects can be approximated by the summation of a set of finite poisson mixtures simulation study shows that the mhd estimates perform satisfactorily for data without outlying observation s and outperform the reml estimates when data are contaminated application to a data set of recurrent urinary tract infections uti with random institution effects demonstrates the practical use of the robust mhd estimation method

residual diagnostics for mixture models abstract a sample is commonly modeled by a mixture distribution if the observations follow a common distribution but the parameter of interest differs between observations for example we observe the lengths but not the ages of a sample offish it may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish provided there is more than one age class in the sample then the data are distributed as a mixture of normals in this article we assume that the data are a random sample from a mixture of exponential family distributions and that for each observation the parameter of interest is sampled independently from an unknown mixing distribution q the adequacy of a fitted mixture model can be assessed by examining residuals based on the ratio of the observed to expected fit residuals based on the homogeneity model in which q is a one point distribution display a convexity property when the data follow a mixture model this becomes the basis fo

subsampling and model selection in time series analysis in this paper the subsampling method of carlstein 1986 is used to estimate the risk of prediction for time series data we extend carlstein s result by proving strong consistency of the subsampling estimator and we propose a procedure for selecting a time series model empirically from a set of possibly nonnested and misspecified models by using estimated risk of prediction as a selection criterion when this procedure is applied to the selection of the order of an autoregressive model it is shown to be a consistent order selector if an appropriate subsample size is chosen we propose a practical model selection procedure with a common subsample size chosen by hall jing s 1996 procedure

richardson extrapolation and the bootstrap abstract simulation methods particularly efron s 1979 bootstrap are being applied more and more frequently in statistical inference given data x 1 xn distributed according to p which belongs to a hypothesized model p the basic goal is to estimate the distribution l p of a function tn x 1 xn p the bootstrap presupposes the existence of an estimate and involves estimating l p by the distribution l n of where x 1 xn is distributed according to the method is of particular interest when ln though known in principle can realistically only be computed by simulation such computation can be expensive if n is large and tn is complex e g see the multivariate goodness of fit tests of beran and millar 1986 even when bootstrap application to a single data set is not excessively expensive monte carlo studies of the bootstrap are another matter we propose a method based on the classical ideas of richardson extrapolation for reducing the computational cost inherent in bootstra

assessing isotropy for spatial point processes summary a common assumption while analyzing spatial point processes is direction invariance i e isotropy in this article we propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second order intensity function we derive an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample second order intensity function and use this to construct a test statistic with a 2 limiting distribution we demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set where our approach confirms suspected directional effects in the spatial distribution of the desert plant species

a thinned block bootstrap variance estimation procedure for inhomogeneous spatial point patterns when modeling inhomogeneous spatial point patterns it is of interest to fit a parametric model for the first order intensity function foif of the process in terms of some measured covariates estimates for the regression coefficients say can be obtained by maximizing a poisson maximum likelihood criterion little work has been done on the asymptotic distribution of except in some special cases in this article we show that is asymptotically normal for a general class of mixing processes to estimate the variance of we propose a novel thinned block bootstrap procedure that assumes that the point process is second order reweighted stationary to apply this procedure only the foif and not any high order terms of the process needs to be estimated we establish the consistency of the resulting variance estimator and demonstrate its efficacy through simulations and an application to a real data example

recent developments in computer assisted analysis of mixtures this paper reviews recent developments in the area of computer assisted analysis of mixture distributions c a man given a biometric situation of interest in which under homogeneity assumptions a certain parametric density occurs such as the poisson the binomial the geometric the normal and so forth then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population this situation is called unobserved heterogeneity this naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest since it also incorporates the homogeneous situations as a special case besides developments in theory and algorithms the work focuses on developments in biometric applications such as meta analysis fertility studies estimation of prevalence under clustering and estimation of the distribution function of survival time under interval censoring the approach is nonparametric for the mixing distribution including leaving the number of components subpopulations of the mixing distribution unknown

inference for linear models with dependent errors summary the paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors theoretically we obtain asymptotic normality for the m estimator of the regression parameter under mild conditions and establish a uniform bahadur representation for recursive m estimators methodologically we extend the recently proposed self normalized approach of shao from stationary time series to the regression set up where the sequence of response variables is typically non stationary in mean since the limiting distribution of the self normalized statistic depends on the design matrix and its corresponding critical values are case dependent we develop a simulation based approach to approximate the critical values consistently through a simulation study we demonstrate favourable finite sample performance of our method in comparison with a block bootstrap based approach empirical illustrations using two real data sets are also provided

bias corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling summary we introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes for variance estimation our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval we show that they can achieve better rates in mean squared error than the usual subsampling variance estimator in particular for n n observation windows the optimal rate of n 2 can be achieved if the data have a finite dependence range for hypothesis testing we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics we assess the numerical performance of the proposed methods through simulation and apply them to analyze a tropical forest data set

on blocking rules for the bootstrap with dependent data summary we address the issue of optimal block choice in applications of the block bootstrap to dependent data it is shown that optimal block size depends significantly on context being equal to n 3 n 4 and nll5 in the cases of variance or bias estimation estimation of a onesided distribution function and estimation of a two sided distribution function respectively a clear intuitive explanation of this phenomenon is given together with outlines of theoretical arguments in specific cases it is shown that these orders of magnitude of block sizes can be used to produce a simple practical rule for selecting block size empirically that technique is explored numerically

window subsampling of estimating functions with application to regression models abstract we propose a subsampling method for estimating the asymptotic standard error of a statistic n that is the solution to an estimating equation 1 n n j 1 uj y j xj 0 where the data yj may be temporally or spatially correlated and the estimating function may depend on covariates xj a key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence the availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data the methods that we develop extend the subsampling ideas of carlstein sherman and garcia soidan and hall to estimating functions our approach provides an attractive alternative to the jackknife method of lele particularly for large datasets because we do not require parameter reestimation

mixed poisson regression models with covariate dependent rates this paper studies a class of poisson mixture models that includes covariates in rates this model contains poisson regression and independent poisson mixtures as special cases estimation methods based on the em and quasi newton algorithms properties of these estimates a model selection procedure residual analysis and goodness of fit test are discussed a monte carlo study investigates implementation and model choice issues this methodology is used to analyze seizure frequency and ames salmonella assay data

on sample reuse methods for dependent data we suggest a sample reuse method for dependent data based on a cross between the block bootstrap and richardson extrapolation instead of simulating a same size resample by resampling blocks and placing them end to end it analyses the blocks directly and employs a variant of richardson extrapolation to adjust for block size a simple empirical rule also based on richardson extrapolation is suggested for empirically selecting the block size performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal