block bootstraps for time series with fixed regressors this article examines block bootstrap methods in linear regression models with weakly dependent error variables and nonstochastic regressors contrary to intuition the tapered block bootstrap tbb with a smooth taper not only loses its superior bias properties but may also fail to be consistent in the regression problem a similar problem albeit at a smaller scale is shown to exist for the moving and the circular block bootstrap mbb and cbb respectively as a remedy an additional block randomization step is introduced that balances out the effects of nonuniform regression weights and restores the superiority of the modified tbb the randomization step also improves the mbb or cbb interestingly the stationary bootstrap sb automatically balances out regression weights through its probabilistic blocking mechanism without requiring any modification and enjoys a kind of robustness optimal block sizes are explicitly determined for block bootstrap variance estimators under regression finite sa

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

a fast subsampling method for nonlinear dynamic models abstract we highlight a fast subsampling method that can be used to provide valid inference in nonlinear dynamic econometric models this method is based on the subsampling theory proposed by politis and romano a general theory for large sample confidence regions based on subsamples under minimal assumptions technical report 399 dept of statistics stanford university large sample confidence regions based on subsamples under minimal assumptions annals of statistics 22 2031 2050 fast subsampling directly exploits score functions computed on each subsample and avoids recomputing the estimators for each of them this method is used to approximate the limit distribution of estimators possibly simulation based that admit an asymptotic linear representation with both known and unknown rates of convergence monte carlo experiments demonstrate the desirable performance and vast improvement in the numerical speed of the fast subsampling method

on positive solutions for some semilinear periodic parabolic eigenvalue problems for a bounded domain in rn n 2 satisfying a weak regularity condition we study existence of positive and t periodic weak solutions for the periodic parabolic problem lu g x t u in r u 0 on r we characterize the set of positive eigenvalues with positive eigenfunctions associated under the assumptions that g is a caratheodory function such that g x t is nonincreasing in 0 a e x t r satisfying some integrability conditions in x t and 0tesssupx inf 0g x t dt 0

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

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

on a multicommodity stochastic flow network with unreliable nodes subject to budget constraint from the quality management and decision making view point reliability and unreliability are important indices to measure the quality level for a stochastic flow network in a multicommodity stochastic flow network with unreliable nodes the branches and nodes all have several possible capacities and may fail different types of the commodity which are transmitted through the same network simultaneously compete the capacities of branches and nodes in this paper we first define the system capacity as a vector for a multicommodity stochastic flow network with unreliable nodes then we design a performance index which is the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint it can be applied to evaluate the quality level for such a network a simple approach based on minimal cuts is thus presented to evaluate the performance index

a note on fitting a marginal model to mixed effects log linear regression data via gee marginal generalized linear models for correlated data are often fit by generalized estimating equations liang k y and zeger s l 1986 biometrika 73 13 22 which requires the marginal expectation to be correctly specified while the covariance structure is allowed to be misspecified this note is concerned with the correct specification of the marginal mean for data from a mixed log linear regression model and the relationship between the true subject specific parameters and the true marginal parameters

maximum likelihood and the bootstrap for nonlinear dynamic models we provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes we apply our results to the moving blocks bootstrap of kunsch ann stat 17 1989 1217 and liu and singh in r lepage l billiard eds exploring the limits of the bootstrap wiley new york 1992 and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of quasi maximum likelihood estimators we also consider bootstrap testing in particular we prove the first order asymptotic validity of the bootstrap distribution of suitable bootstrap analogs of wald and lagrange multiplier statistics for testing hypotheses

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

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

delay dependent stability for uncertain stochastic neural networks with time varying delay abstract this paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with time varying delay the parameter uncertainties are assumed to be norm bounded by defining a new lyapunov krasovskii functional the restrictions such as the time varying delay was required to be differentiable and its derivative was strictly smaller than one are removed based on the linear matrix inequality approach delay dependent stability criteria are obtained such that for all admissible uncertainties the stochastic neural network is globally asymptotically stable in the mean square two slack variables are introduced into the obtained stability criteria to reduce the conservatism finally a numerical example is given to illustrate the effectiveness of the developed method

a latent process regression model for spatially correlated count data summary this paper proposes a regression model for spatially correlated count data that generalizes the work spatially correlated count data arise in a variety of settings frequently it is of interest to make marginal inferences about spatial trends and effects of explanatory variables on spatially correlated counts an example application described in this paper involves an examination of the distribution of neuronal cells in a laboratory culture well our motivation for examining the distribution of cells was due to the implications of the distribution for the choice of an efficient sampling method to estimate total cell count total neuronal cell counts in a culture well are ordinarily estimated using data from multiple sampled subregions viewed under the microscope or with the aid of an image analysis system because counting all cells in a culture well is prohibitively time consuming as routine practice these sampling methods typically involve recording from multiple randomly selected fields the area of the field and number of cells visible in the field a cell per unit area density is estimated from the data and the total cell count estimate for the well is obtained by multiplication by the total well area these methods implicitly assume that cells are distributed completely at random throughout the well experience would suggest that there could be trends in neuron density and clustering tendencies for example neurons can tend to a higher density in the center of a well due to a slight vortex that occurs when the cultures are moved before the neurons have attached themselves to the substratum neurons also may distribute in higher density around the edges of a culture well due to a meniscus and slightly greater depth of medium at the edge of a well spatial clustering may result if neural cell bodies migrate along the cell body s neuritic processes or if the tissue culture tray is

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

nonparametric estimation of the moments of a general statistic computed from spatial data abstract a statistic s is computed on spatially indexed data x i i d where d is a finite subset of the integer lattice z2 we propose a simple nonparametric method for estimating the moments e g variance skewness of s d using only the observed data at hand the method uses replicates of s computed on smaller subsets of d no explicit knowledge of the underlying spatial dependence mechanism is needed and the marginal distribution of x i may also be unknown the shape of d can be quite irregular and s is allowed to be a general statistic the proposed estimator is shown to be consistent and asymptotically normal under mild conditions on s d and mixing conditions on the strength of spatial dependence as a numerical example the estimator is used in assessing the geographic clumping of cancer deaths in the united states

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

a general theory for jackknife variance estimation the delete 1 jackknife is known to give inconsistent variance estimators for nonsmooth estimators such as the sample quantiles this well known deficiency can be rectified by using a more general jackknife with d the number of observations deleted depending on a smoothness measure of the point estimator our general theory explains why jackknife works or fails it also shows that i for sufficiently smooth estimators the jackknife variance estimators with bounded d are consistent and asymptotically unbiased and ii for nonsmooth estimators d has to go to infinity at a rate explicitly determined by a smoothness measure to ensure consistency and asymptotic unbiasedness improved results are obtained for several classes of estimators in particular for the sample p quantiles the jackknife variance estimators with d satisfying n 1 2 d rightarrow 0 and n d rightarrow infty are consistent and asymptotically unbiased

on the existence of multiple ordered solutions of nonlinear eigenvalue problems on etudie le probleme de dirichlet u f u dans u o sur ou est un domaine borne lisse de r n n 1 la fonction a valeur reelle f o r est supposee c 1 et o est un parametre reel on etudie le lien entre les changements de signe de la fonction f et l existence de plusieurs solutions positives ordonnees

jackknifing linear estimating equations asymptotic theory and applications in stochastic processes let x1 x2 x be a vector of possibly dependent random variables having distribution f x 0 let g x 0 e 1 gi x 0 0 be an estimating equation for 0 e g the score function or the maximum pseudolikelihood estimating equation in spatial processes let o n be the estimator obtained from g such that 0on 0o in probability and n 1 2 0 00 n o v in distribution in many situations it is difficult to derive an analytical expression for v e g for maximum pseudolikelihood estimators for the spatial processes in this paper we give a jackknife estimator of v and show that it is weakly consistent the method consists of deleting one estimating equation instead of one observation at a time and thus obtaining the pseudovalues the method of proof and conditions are similar to those of reeds with some modifications the method applies equally to independent and identically distributed random variables independent but not identically distributed random variables timeor space dependent stochastic processes our conditions are less severe than carlstein s who deals with a similar problem of estimating v for dependent observations we also give some simulation results

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

on the asymptotic properties of the jackknife histogram we study the asymptotic normality of the jackknife histogram for one sample mean it holds if and only if r the number of observations retained and d n r the number of observations deleted both diverge to infinity the best convergence rate n 1 2 is obtained when r o n and d o n for u statistics of degree 2 and nonlinear statistics admitting a certain expansion similar results are obtained under conditions on r and d a second order approximation based on the edgeworth expansion is discussed

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

internet packet routing application of a k quickest path algorithm this paper describes a study on the application of an algorithm to rank the k quickest paths to the routing of data packets in internet networks for this purpose an experimental framework was developed by considering two types of random generated networks to simulate values of the ip packet sizes a truncated pareto distribution was defined having in mind to reflect a key feature of internet traffic namely its self similar stochastic nature results concerning the average cpu times of the algorithm for the different sets of experiments will be presented and discussed

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

estimating equations for spatially correlated data in multi dimensional space summary we use the quasilikelihood concept to propose an estimating equation for spatial data with correlation across the study region in a multi dimensional space with appropriate mixing con ditions we develop a central limit theorem for a random field under various lp metrics the consistency and asymptotic normality of quasilikelihood estimators can then be derived we also conduct simulations to evaluate the performance of the proposed estimating equation and a dataset from east lansing woods is used to illustrate the method

reliability evaluation of a revised stochastic flow network with uncertain minimum time abstract this paper constructs a revised stochastic flow network to model a realistic computer network in which each arc has a lead time and a stochastic capacity the minimum time to send a specified amount of data through the network is thus uncertain hence this paper mainly proposes an approach for evaluating the system reliability that d units of data can be transmitted through k minimal paths simultaneously within the time threshold t the idea of lower boundary points for d t the minimal system states satisfying the demand d within the time threshold t is proposed firstly all system states meeting the time and demand requirements can be represented as the union of subsets generated from all lower boundary points for d t and thus the system reliability is computed quickly

subsampling inference in threshold autoregressive models this paper discusses inference in self exciting threshold autoregressive setar models of main interest is inference for the threshold parameter it is well known that the asymptotics of the corresponding estimator depend upon whether the setar model is continuous or not in the continuous case the limiting distribution is normal and standard inference is possible in the discontinuous case the limiting distribution is non normal and it is not known how to estimate it consistently we show that valid inference can be drawn by the use of the subsampling method moreover the method can even be extended to situations where the dis continuity of the model is unknown in this case the inference for the regression parameters of the model also becomes difficult and subsampling can be used again in addition we consider an hypothesis test for the continuity of a setar model a simulation study examines small sample performance and an application illustrates how the proposed methodology works in practice

variance estimation for statistics computed from spatial lattice data summary a statistic s is computed on spatially indexed data x i e d where d is a finite subset of the integer lattice 22 we propose a method for estimating the variance and other moments of s by using only the data the set d may be irregularly shaped the statistic s may be arbitrarily complicated and no distributional assumptions marginal or joint are necessary the method uses the statistic computed on overlapping subshapes of d as replicates of s the estimator is simply the sample variance of the standardized replicates we demonstrate c2 consistency of the estimator under mild conditions on s and the strength of spatial dependence a rate of convergence is also given giving guidance into the appropriate choice of subshape size and the estimator is illustrated in two data examples

empirical likelihood block bootstrapping monte carlo evidence has made it clear that asymptotic tests based on generalized method of moments gmm estimation have disappointing size the problem is exacerbated when the moment conditions are serially correlated several block bootstrap techniques have been proposed to correct the problem including hall and horowitz 1996 and inoue and shintani 2006 we propose an empirical likelihood block bootstrap procedure to improve inference where models are characterized by nonlinear moment conditions that are serially correlated of possibly infinite order combining the ideas of kitamura 1997 and brown and newey 2002 the parameters of a model are initially estimated by gmm which are then used to compute the empirical likelihood probability weights of the blocks of moment conditions the probability weights serve as the multinomial distribution used in resampling the first order asymptotic validity of the proposed procedure is proven and a series of monte carlo experiments show it may improve test sizes over conventional block bootstrapping

on subsampling estimators with unknown rate of convergence abstract politis and romano have put forth a general subsampling methodology for the construction of large sample confidence regions for a general unknown parameter associated with the probability distribution generating the stationary sequence x 1 x n the subsampling methodology hinges on approximating the large sample distribution of a statistic t n t n x 1 x n that is consistent for at some known rate n although subsampling has been shown to yield confidence regions for of asymptotically correct coverage under very weak assumptions the applicability of the methodology as it has been presented so far is limited if the rate of convergence n happens to be unknown or intractable in a particular setting in this article we show how it is possible to circumvent this limitation by a using the subsampling methodology to derive a consistent estimator of the rate n and b using the estimated rate to construct asymptotically correct confidence regions for based on subsampling

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

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

testing mutual independence between two discrete valued spatial processes a correction to pearson chi squared a common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods in this article we examine the consequences of spatial autocorrelation on pearson s chi squared test of mutual independence between two categorical responses with a general number of classes correspondingly we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation our modified statistic is based on a first order correction factor and thus provides only an approximate test however we show by monte carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest the usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern belgium

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

a composite likelihood approach in fitting spatial point process models we propose a new likelihood based approach in fitting spatial point process models a composite likelihood is first formed by adding some pairwise composite likelihood functions that are defined in terms of the second order intensity function of the underlying process and then used for estimating the unknown parameters the estimation procedure is computationally simple and yields consistent and asymptotically normal estimators under some mild conditions we demonstrate through a simulation study and applications to two real data examples that the proposed approach may lead to improved estimations compared with the commonly used minimum contrast estimation approach

subseries methods in regression abstract we extend subseries methods for stationary sequences to the regression setting to estimate sampling distributions the subseries approach computes the statistic of interest on all possible subseries of a shorter length than the original series and uses the distribution of these replicates to mimic the distribution of the original statistic for proper choice of subseries length the regression parameters can be estimated to order o n 2 3 thus improving on the normal approximation the replicates can also be used to reduce the bias of robust estimators simulation results demonstrate the finite sample effectiveness of the approach for both distribution function estimation and bias reduction applications to spatial data are also discussed

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

higher order improvements of a computationally attractive k step bootstrap for extremum estimators this paper establishes the higher order equivalence of the k step bootstrap introduced recently by davidson and mackinnon 1999 and the standard bootstrap the k step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators such as generalized method of moment and maximum likelihood estimators the paper also extends results of hall and horowitz 1996 to provide new results regarding the higher order improvements of the standard bootstrap and the k step bootstrap for extremum estimators compared to procedures based on first order asymptotics the results of the paper apply to newton raphson nr default nr line search nr and gauss newton k step bootstrap procedures the results apply to the nonparametric iid bootstrap and nonoverlapping and overlapping block bootstraps the results cover symmetric and equal tailed two sided t tests and confidence intervals one sided t tests and confidence intervals wald tests and confidence regions and j tests of over identifying restrictions

analyzing spatially distributed binary data using independent block estimating equations summary we estimate the relation between binary responses and corresponding covariate vectors both observed over a large spatial lattice we assume a hierarchical generalized linear model with probit link function partition the lattice into blocks and adopt the working assumption of independence between the blocks to obtain an easily solved estimating equation standard errors are obtained using the sandwich estimator together with window subsampling sherman 1996 journal of the royal statistical society series b 58 509 523 we apply this to a large data set describing long term vegetation growth together with two other approximate likelihood approaches pairwise composite likelihood cl and estimation under a working assumption of independence the independence and cl methods give similar point estimates and standard errors while the independent block approach gives considerably smaller standard errors as well as more easily interpretable point estimates we present numerical evidence suggesting this increased efficiency may hold more generally

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

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field

analysis of binary spatial data by quasi likelihood estimating equations the goal of this paper is to describe the application of quasi likelihood estimating equations for spatially correlated binary data in this paper a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest with mild assumptions on the correlations the leonov shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses the consistency and asymptotic normality for quasi likelihood estimates can then be derived by modeling spatial correlation with a variogram we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well known example based on data from lansing woods the comparison of generalized estimating equations and the proposed approach is also discussed