residual maximum likelihood reml estimation of a neighbour model for field experiments a spatial analysis of field experiments is proposed which takes account of association between neighbouring plots the residual maximum likelihood reml method of patterson and thompson 1971 biometrika 58 545 554 is used to estimate parameters of a general neighbour model which can be expressed as an autoregressive moving average arma model three data sets are analysed to i highlight the need for a model selection procedure ii illustrate the differing results between incomplete block and neighbour analysis and the effect of including treated border plots in the design and iii illustrate the environmental variation within an experiment using prediction of trend

adjusted qmle for the spatial autoregressive parameter abstract one simple and often very effective way to attenuate the impact of nuisance parameters on maximum likelihood estimation of a parameter of interest is to recenter the profile score for that parameter we apply this general principle to the quasi maximum likelihood estimator qmle of the autoregressive parameter in a spatial autoregression the resulting estimator for has better finite sample properties compared to the qmle for especially in the presence of a large number of covariates it can also solve the incidental parameter problem that arises for example in social interaction models with network fixed effects however spatial autoregressions present specific challenges for this type of adjustment because recentering the profile score may cause the adjusted estimate to be outside the usual parameter space for conditions for this to happen are given and implications are discussed for inference we propose confidence intervals based on a lugannani rice approximation to the distribution of the adjusted qmle of based on our simulations the coverage properties of these intervals are excellent even in models with a large number of covariates

partially observed information and inference about non gaussian mixed linear models in mixed linear models with nonnormal data the gaussian fisher information matrix is called a quasi information matrix quim the quim plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters including the variance components traditionally there are two ways to estimate the information matrix the estimated information matrix and the observed one because the analytic form of the quim involves parameters other than the variance components for example the third and fourth moments of the random effects the estimated quim is not available on the other hand because of the dependence and nonnormality of the data the observed quim is inconsistent we propose an estimator of the quim that consists partially of an observed form and partially of an estimated one we show that this estimator is consistent and computationally very easy to operate the method is used to derive large sample tests of statistical hypotheses that involve the variance components in a non gaussian mixed linear model finite sample performance of the test is studied by simulations and compared with the delete group jackknife method that applies to a special case of non gaussian mixed linear models

a matrix inequality and its statistical application abstract let a 1 a s be nonnegative definite matrices we prove that there are constants c i 1 i s depending on a 1 a s such that for all positive numbers x 1 x s a i c i x i 2 i j 1 s x j a j 2 1 i s where i represents the identity matrix the result is applied to statistical inference about mixed linear models to show the existence of moments of complex estimators including the maximum likelihood and restricted maximum likelihood estimators of the variance components and the empirical best linear unbiased estimators predictors of the fixed random effects

on measuring the variability of small area estimators under a basic area level model summary in this paper based on a basic area level model we obtain second order accurate approxi mations to the mean squared error of model based small area estimators using the fay herriot 1979 iterative method of estimating the model variance based on weighted residual sum of squares we also obtain mean squared error estimators unbiased to second order based on simulations we compare the finite sample performance of our mean squared error estimators with those based on method of moments maximum likelihood and residual maximum likelihood estimators of the model variance our results suggest that the fay herriot method performs better in terms of relative bias of mean squared error estimators than the other methods across different combinations of number of areas pattern of sampling variances and distribution of small area effects we also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second order unbiased for the mean squared error the posterior variance based on such a prior possesses both bayesian and frequentist interpretations

flexible results for quadratic forms with applications to variance components estimation abstract we derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms then describe some applications involving variance components estimation in linear random effects models random effects models and variance components estimation are classical topics in statistics with a corresponding well established asymptotic theory however our finite sample results for quadratic forms provide additional flexibility for easily analyzing randomeffects models in non standard settings which are becoming more important in modern applications e g genomics for instance in addition to deriving novel non asymptotic bounds for variance components estimators in classical linear random effects models we provide a concentration bound for variance components estimators in linear models with correlated random effects our general concentration bound is a uniform version of the hanson wright inequality the main normal approximation result in the paper is derived using reinert and rollin s 2009 embedding technique and multivariate stein s method with exchangeable pairs

likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative summary for submodels of an exponential family we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable first we establish the asymptotic equivalence between the likelihood ratio test and the score test secondly the score test representation is used to derive the asymptotic distribution of the likelihood ratio test these results are derived for general submodels of an exponential family without assuming compactness of the parameter space we then exemplify the results on a class of multivariate normal models where null hypotheses concerning the covariance structure lead to loss of identifi ability of a parameter our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation

constrained estimators and consistency of a regression model on a lexis diagram this article considers a regression model on a lexis diagram of an a p table with a single response in each cell following a distribution in the exponential family a regression model on the fixed effects of a rows p columns and a p 1 diagonals induces a singular design matrix and yields multiple estimators leading to parameter identifiability problem in age period cohort analysis in social sciences demography and epidemiology where assessment of secular trend in age period and birth cohort of social events e g violence and diseases e g cancer is of interest similar problems also exist in other settings such as in supersaturated designs in this article we study the finite sample properties of the multiple estimators propose a penalized profile likelihood method to study the consistency and asymptotic bias and demonstrate the results through simulations and data analysis as a by product the identifiability problem is addressed with consistent estimation for model parameters an

heteroscedastic one way anova and lack of fit tests recent articles have considered the asymptotic behavior of the one way analysis of variance anova f statistic when the number of levels or groups is large in these articles the results were obtained under the assumption of homoscedasticity and for the case when the sample or group sizes ni remain fixed as the number of groups a tends to infinity in this article we study both weighted and unweighted test statistics in the heteroscedastic case the unweighted statistic is new and can be used even with small group sizes we demonstrate that an asymptotic approximation to the distribution of the weighted statistic is possible only if the group sizes tend to infinity suitably fast in relation to a our investigation of local alternatives reveals a similarity between lack of fit tests for constant regression in the present case of replicated observations and the case of no replications which uses smoothing techniques the asymptotic theory uses a novel application of the projection principle to obtain

closed form approximations to the reml estimator of a variance ratio or heritability in a mixed linear model in this article we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation in most applications the commonly used restricted maximum likelihood reml estimator can only be obtained via an iterative approach in some cases the algorithm used to compute reml estimates may be slow or may even fail to converge we develop a set of closed form approximations to the reml estimator and the performance of these estimators is compared with that of the reml estimator we provide guidelines regarding how to choose the estimator that best approximates the reml estimator examples presented in the article suggest that the closed form estimators compete with and in some cases outperform the reml estimator

wald consistency and the method of sieves in reml estimation we prove that for all unconfounded balanced mixed models of the analysis of variance estimates of variance components parameters that maximize the restricted gaussian likelihood are consistent and asymptotically normal and this is true whether normality is assumed or not for a general nonnormal mixed model we show estimates of the variance components parameters that maximize the restricted gaussian likelihood over a sequence of approximating parameter spaces i e a sieve constitute a consistent sequence of roots of the reml equations and the sequence is also asymptotically normal the results do not require the rank p of the design matrix of fixed effects to be bounded an example shows that in some unbalanced cases estimates that maximize the gaussian likelihood over the full parameter space can be inconsistent given the condition that ensures consistency of the sieve estimates 1 introduction in many cases exploration of asymptotic properties of maximum likelihood ml estimates led to one of two types of consistency cramer 1946 or wald 1949 types the former establishes the consistency of some root of the likelihood equation s but usually gives no indication on how to identify such a root when the roots of the likelihood equation s are

estimation of mutual information using kernel density estimators mutual information is useful for investigating the dependence between two experimental time series it is often used to establish an appropriate time delay in phase portrait reconstruction from time series data a histogram based approach has been used so far to estimate the probabilities it is shown here that kernel density estimation of the probability density functions needed in estimating the average mutual information across two coordinates can be more effective than the histogram method of fraser and swinney phys rev a 33 1134 1986

measuring explained variation in linear mixed effects models we generalize the well known r2 measure for linear regression to linear mixed effects models our work was motivated by a cluster randomized study conducted by the eastern cooperative oncology group to compare two different versions of informed consent document we quantify the variation in the response that is explained by the covariates under the linear mixed model and study three types of measures to estimate such quantities the first type of measures make direct use of the estimated variances the second type of measures use residual sums of squares in analogy to the linear regression the third type of measures are based on the kullback leibler information gain all the measures can be easily obtained from software programs that fit linear mixed models we study the performance of the measures through monte carlo simulations and illustrate the usefulness of the measures on data sets copyright 2003 john wiley sons ltd

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

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

generalized score test of homogeneity for mixed effects models many important problems in psychology and biomedical studies require testing for overdispersion correlation and heterogeneity in mixed effects and latent variable models and score tests are particularly useful for this purpose but the existing testing procedures depend on restrictive assumptions in this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero under some mild conditions not only do we derive asymptotic distributions of the test statistics but also propose a resampling procedure for approximating their asymptotic distributions conditional on the observed data to overcome the technical challenge we establish an invariance principle for random quadratic forms indexed by a parameter a simulation study is conducted to investigate the empirical performance of the test statistics a real data set is analyzed to illustrate the application of our theoretical results

goodness of fit tests for mixed model diagnostics a simple goodness of fit test is proposed for checking distributional assumptions involved in a mixed linear model an estimated critical value of the test statistic is derived and is shown to be asymptotically correct under mild conditions as a special case the test may be applied to linear regression models to formally check distribution of the errors finite sample performance of the proposed test is examined and compared with that of a previously proposed test by simulations

evidence for conformal invariance of crop yields the aim of this paper is to study the nature of spatial correlation of yields of agricultural crops the focus is primarily on natural or non anthropogenic spatial variation patterns that cannot be explained by topography by variety or treatment effects or by agricultural practices conformal invariance implies stationarity and isotropy and also determines the rate of decay of spatial correlations the resulting gaussian model is studied empirically to see whether it describes satisfactorily the pattern of spatial correlations observed in field trials of various crops by embedding the law in a larger

a new class of average moment matching priors summary we derive a new class of priors for the variance component in the fay herriot model a mixed regression model widely used in small area estimation this class includes the well known uniform or superhannonic prior through simulation we illustrate the use of our class of priors

estimating mutual information we present two classes of improved estimators for mutual information m x y from samples of random points distributed according to some joint probability density mu x y in contrast to conventional estimators based on binnings they are based on entropy estimates from k nearest neighbor distances this means that they are data efficient with k 1 we resolve structures down to the smallest possible scales adaptive the resolution is higher where data are more numerous and have minimal bias indeed the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale giving typically systematic errors which scale as functions of k n for n points numerically we find that both families become exact for independent distributions i e the estimator m x y vanishes up to statistical fluctuations if mu x y mu x mu y this holds for all tested marginal distributions and for all dimensions of x and y in addition we give estimators for redundancies between more than two random variables we compare our algorithms in detail with existing algorithms finally we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis ica for improving ica and for estimating the reliability of blind source separation

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

asymptotics for analysis of variance when the number of levels is large abstract we study asymptotic results for f tests in analysis of variance models as the number of factor levels goes to but the number of observations for each factor combination is fixed asymptotic derivations of the type discussed in this article would be relevant whenever both the numerator and denominator degrees of freedom go to at the same rate we consider null and alternative distributions of f the usual f statistic for fixed effects and random effects balanced and unbalanced one way and two way and normal and nonnormal analysis of variance anova models the results may be most relevant for random effects and mixed models for example we may have an agricultural experiment in which the number of cows is quite large but the number of measurements on each cow is small the results would also be relevant for fixed effects models in which there are many factor levels but not many observations for each factor level

asymptotic normality of the anova estimates of components of variance in the nonnormal unbalanced hierarchal mixed model on considere le plan hierarchique non equilibre non normal et on donne des conditions douces pour une suite de tels plans telle que le vecteur d estimations anova normalisees converge vers une distribution normale multivariable

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

incidental versus random nuisance parameters let p vartheta eta vartheta eta in theta times h with theta subset mathbb r and h arbitrary be a family of mutually absolutely continuous probability measures on a measurable space x mathscr a the problem is to estimate vartheta based on a sample x 1 cdots x n from times n 1 p vartheta eta nu if eta 1 cdots eta n are independently distributed according to some unknown prior distribution gamma then the distribution of n 1 2 vartheta n vartheta under p n vartheta gamma p vartheta gamma being the gamma mixture of p vartheta eta eta in h cannot be more concentrated asymptotically than a certain normal distribution with mean 0 say n 0 sigma 2 0 vartheta gamma folklore says that such a bound is also valid if eta 1 cdots eta n are just unknown values of the nuisance parameter in this case the distribution cannot be more concentrated asymptotically than n 0 sigma 2 0 vartheta e n eta 1 cdots eta n where e n eta 1 cdots eta n is the empirical distribution of eta 1 cdots eta n the purpose of the present paper is to discuss to which extent this conjecture is true the results are summarized at the end of sections 1 and 3

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

linear models for field trials smoothing and cross validation abstract spatial methods for the analysis of agricultural field experiments are represented here as smoothing methods applied simultaneously with the estimation of treatment effects selection of both the form of the smoother and the degree of smoothing required may be based on cross validation particular emphasis is placed in this paper on generalized least squares estimation ion linear models but the principle applies quite generally keywords agricultural field experiments generalized least squares incomplete block designs neighbour methods papadakis method recovery of inter block formation smoothing and spatial models

binary time series modeling with application to adhesion frequency experiments repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion cell adhesion plays an important role in many physiological and pathological processes traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent bernoulli trials this assumption often can be violated in practice motivated by the analysis of repeated adhesion tests a binary time series model incorporating random effects is developed a goodness of fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects the asymptotic distribution of the goodness of fit statistic is derived and its finite sample performance is examined through a simulation study application of the proposed methodology to real data from a t cell experiment reveals some interesting information including the dependency between repeated adhesion tests

independent and identically distributed monte carlo algorithms for semiparametric linear mixed models hybrid versions of independent and identically distributed weighted chinese restaurant wcr algorithms are developed for inference in semiparametric linear mixed models under minimal assumptions for the random effects distributions the wcr method of working with the posterior partition structure leads to rao blackwell estimates for higher order moments of random effects such as skewness and kurtosis and can be used to estimate densities for random effects a key feature of our approach is the manner in which we incorporate external estimates into our algorithms the use of such information leads to simplified computational procedures reduces the amount of user input required for specifying models and results in numerical stability and accuracy the resulting procedures are automated and can be readily used in standard statistical software our methods are tested by simulation and illustrated by application to a longitudinal study involving chronic renal disease

noncentral limit theorems for quadratic forms in random variables having long range dependence we study the weak convergence in d lbrack 0 1 rbrack of the quadratic form sum lbrack nt rbrack j 1 sum lbrack nt rbrack k 1 a j k h m x j h m x k adequately normalized here a s infty s infty is a symmetric sequence satisfying sum a s infty h m is the m th hermite polynomial and x j j geq 1 is a normalized gaussian sequence with covariances r k sim k d l k as k rightarrow infty where 0 d 1 and l is slowly varying we prove that for all m geq 1 the limit is brownian motion when 1 2 d 1 and it is the non gaussian rosenblatt process when 0 d 1 2

whitening as a tool for estimating mutual information in spatiotemporal data sets we address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites the well known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations i e at whitening the data such that it is replaced by spatiotemporal innovations this approach provides a link to the maximum likelihood method and for appropriately chosen models removes the problem of estimating probability distributions of unknown possibly complicated shape a parsimonious multivariate autoregressive model based on nearest neighbour interactions is employed mutual information can be reinterpreted in the framework of dynamical model comparison i e likelihood ratio testing since it is shown to be equivalent to the difference of the log likelihoods of coupled and uncoupled models for a pair of sites and a parametric estimator of mutual information can be derived we also discuss within the framework of model comparison the relationship between the coefficient of linear correlation and mutual information the practical application of this methodology is demonstrated for simulated multivariate time series generated by a stochastic coupled map lattice the parsimonious modelling approach is compared to general multivariate autoregressive modelling and to independent component analysis ica

on the asymptotic distribution of quadratic forms in uniform order statistics on utilise des conditions minimales sur la suite des formes pour montrer que la distribution limite est la convolution d une somme de khi deux non centres ponderes et d une variable normale

mean squared error of empirical predictor the term empirical predictor refers to a two stage predictor of a linear combination of fixed and random effects in the first stage a predictor is obtained but it involves unknown parameters thus in the second stage the unknown parameters are replaced by their estimators in this paper we consider mean squared errors mse of empirical predictors under a general setup where ml or reml estimators are used for the second stage we obtain second order approximation to the mse as well as an estimator of the mse correct to the same order the general results are applied to mixed linear models to obtain a second order approximation to the mse of the empirical best linear unbiased predictor eblup of a linear mixed effect and an estimator of the mse of eblup whose bias is correct to second order the general mixed linear model includes the mixed anova model and the longitudinal model as special cases

estimation and hypothesis testing for collections of autoregressive time series summary the analysis of a number of independent first order autoregressive time series is considered in a normal theory context a model is studied which allows for nonstationary and nonidentical distribution of the series caused by both fixed effect and random effect components

a solution to the dynamical inverse problem of eeg generation using spatiotemporal kalman filtering we present a new approach for estimating solutions of the dynamical inverse problem of eeg generation in contrast to previous approaches we reinterpret this problem as a filtering problem in a state space framework for the purpose of its solution we propose a new extension of kalman filtering to the case of spatiotemporal dynamics the temporal evolution of the distributed generators of the eeg can be reconstructed at each voxel of a discretisation of the gray matter of brain by fitting linear autoregressive models with neighbourhood interactions to eeg time series new classes of inverse solutions with improved resolution and localisation ability can be explored for the purposes of model comparison and parameter estimation from given data we employ a likelihood maximisation approach both for instantaneous and dynamical inverse solutions we derive estimators of the time dependent estimation error at each voxel the performance of the algorithm is demonstrated by application to simulated and clinical eeg recordings it is shown that by choosing appropriate dynamical models it becomes possible to obtain inverse solutions of considerably improved quality as compared to the usual instantaneous inverse solutions

visible evidence for the birch and swinnerton dyer conjecture for modular abelian varieties of analytic rank zero this paper provides evidence for the birch and swinnerton dyer conjecture for analytic rank 0 abelian varieties a f that are optimal quotients of j 0 n attached to newforms we prove theorems about the ratio l a f 1 af develop tools for computing with af and gather data about certain arithmetic invariants of the nearly 20 000 abelian varieties a f of level 2333 over half of these a f have analytic rank 0 and for these we compute upper and lower bounds on the conjectural order of iii a f we find that there are at least 168 such af for which the birch and swinnerton dyer conjecture implies that iii a f is divisible by an odd prime and we prove for 37 of these that the odd part of the conjectural order of iii a f really divides iii a f by constructing nontrivial elements of iii a f using visibility theory we also give other evidence for the conjecture the appendix by cremona and mazur fills in some gaps in the theoretical discussion in their paper on visibility of shafarevich tate groups of elliptic curves

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

iterative estimating equations linear convergence and asymptotic properties we propose an iterative estimating equations procedure for analysis of longitudinal data we show that under very mild conditions the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity furthermore we show that the limiting estimator is consistent and asymptotically efficient as expected the method applies to semiparametric regression models with unspecified covariances among the observations in the special case of linear models the procedure reduces to iterative reweighted least squares finite sample performance of the procedure is studied by simulations and compared with other methods a numerical example from a medical study is considered to illustrate the application of the method

spatio temporal structure in coupled map lattices two point correlations versus mutual information a one dimensional lattice of logistic maps is investigated in the case of strong nonlinearity and strong coupling although the dynamics may be classified as fully developed turbulence spatio temporal structure can be detected by computing time delayed mutual information and two point correlations the correlation is found to be superior in detecting weak structure an improved algorithm for mutual information is described

testing for covariate effects in the fully nonparametric analysis of covariance model traditional inference questions in the analysis of covariance mainly focus on comparing different factor levels by adjusting for the continuous covariates which are believed to also exert a significant effect on the outcome variable testing hypotheses about the covariate effects although of substantial interest in many applications has received relatively limited study in the semiparametric nonparametric setting in the context of the fully nonparametric analysis of covariance model of akritas et al we propose methods to test for covariate main effects and covariate factor interaction effects the idea underlying the proposed procedures is that covariates can be thought of as factors with many levels the test statistics are closely related to some recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large the limiting normal distributions are established under the null hypotheses and local alternatives by asymptotically approximating a new class

on the existence and uniqueness of the maximum likelihood estimate of a vector valued parameter in fixed size samples the maximum likelihood estimate is shown to exist and to be unique if a twice continuously differentiable likelihood function is constant on the boundary of the parameter space and if the hessian matrix is negative definite whenever the gradient vector vanishes the condition of constancy on the boundary cannot be completely removed cf tarone and gruenhage 1975 the theory is illustrated with several examples

fence methods for mixed model selection many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure asymptotic properties for these types of procedures in settings like linear regression and arma time series have been studied but these do not naturally extend to nonstandard situations such as mixed effects models where simple definition of the sample size is not meaningful this paper introduces a new class of strategies known as fence methods for mixed model selection which includes linear and generalized linear mixed models the idea involves a procedure to isolate a subgroup of what are known as correct models of which the optimal model is a member this is accomplished by constructing a statistical fence or barrier to carefully eliminate incorrect models once the fence is constructed the optimal model is selected from among those within the fence according to a criterion which can be made flexible in addition we propose two variations of the fence the first is a stepwise procedure to handle situations of many predictors the second is an adaptive approach for choosing a tuning constant we give sufficient conditions for consistency of fence and its variations a desirable property for a good model selection procedure the methods are illustrated through simulation studies and real data analysis

testing for nonlinearity in high dimensional time series from continuous dynamics abstract we address the issue of testing for nonlinearity in time series from continuous dynamics and propose a quantitative measure for nonlinearity which is based on discrete parametric modelling the well known problems of modelling continuous dynamical systems by discrete models are addressed by a subsampling approach this measure should preferably be combined with conventional surrogate data testing the performance of the test is demonstrated by application to simulated heavily noise contaminated time series from high dimensional lorenz systems and to experimental time series from a high dimensional mode of taylor couette flow we also discuss the discrimination power of the test under surrogate data testing when compared with other well tried test statistics

a unified jackknife theory for empirical best prediction with m estimation the paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases the paper develops jackknife theory for the important but so far neglected prediction problem for the general mixed model for estimation of fixed parameters a jackknife method is considered for a general class of m estimators which includes the maximum likelihood residual maximum likelihood and anova estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models for both the prediction and estimation problems a jackknife method is used to obtain estimators of the mean squared errors mse asymptotic unbiasedness of the mse estimators is shown to hold essentially under certain moment conditions simulation studies undertaken support our theoretical results 1 introduction due to the advent of high speed computers and powerful software computer oriented statistical methods including various resampling methods have received considerable attention in recent years as statisticians are constantly facing complex problems the jackknife method is one such simple resampling method which is very popular among survey samplers primarily due