a regression method for spatial disease rates an estimating function approach abstract epidemiologists commonly study the geographical variation of disease rates to generate and refine testable hypotheses regarding etiology poisson regression is often used to estimate the parameters that characterize the effects of risk factors on disease hierarchical models have been proposed to utilize spatial locations and neighbors as surrogates for unknown or unmeasured risk factors in the analysis of disease rates although hierarchical models are useful in modeling spatial disease rates in a scientifically meaningful way the analytic tools for them are generally computationally intensive we overcome this issue by applying a conditional spatial modeling technique using unbiased estimating functions the resulting estimator of regression coefficients is consistent and asymptotically normally distributed under mild conditions a simulation study compares the performance of the proposed scheme with the approximate inference methods for hierarchical models we apply the proposed scheme to sco

autoregressive spatial smoothing and temporal spline smoothing for mapping rates this article proposes generalized additive mixed models for the analysis of geographic and temporal variability of mortality rates this class of models accommodates random spatial effects and fixed and random temporal components spatiotemporal models that use autoregressive local smoothing across the spatial dimension and b spline smoothing over the temporal dimension are developed the objective is the identification of temporal trends and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time regions with consistently high rate estimates may be followed for further investigation the methodology is illustrated by analysis of british columbia infant mortality data

a mixed mover stayer model for spatiotemporal two state processes studies of recurring infection or chronic disease often collect longitudinal data on the disease status of subjects two state transitional models are useful for analysis in such studies where at any point in time an individual may be said to occupy either a diseased or disease free state and interest centers on the transition process between states here two additional features are present the data are spatially arranged and it is important to account for spatial correlation in the transitional processes corresponding to different subjects in addition there are subgroups of individuals with different mechanisms of transitions these subgroups are not known a priori and hence group membership must be estimated covariates modulating transitions are included in a logistic additive framework inference for the resulting mixture spatial markov regression model is not straightforward we develop here a monte carlo expectation maximization algorithm for maximum likelihood estimation and a markov chain monte carlo sampling scheme for summarizing the posterior distribution in a bayesian analysis the methodology is applied to a study of recurrent weevil infestation in british columbia forests

on consistency and sparsity for principal components analysis in high dimensions principal components analysis pca is a classic method for the reduction of dimensionality of data in the form of n observations or cases of a vector with p variables contemporary datasets often have p comparable with or even much larger than n our main assertions in such settings are a that some initial reduction in dimensionality is desirable before applying any pca type search for principal modes and b the initial reduction in dimensionality is best achieved by working in a basis in which the signals have a sparse representation we describe a simple asymptotic model in which the estimate of the leading principal component vector via standard pca is consistent if and only if p n n 0 we provide a simple algorithm for selecting a subset of coordinates with largest sample variances and show that if pca is done on the selected subset then consistency is recovered even if p n n

asymptotics of empirical eigenstructure for high dimensional spiked covariance we derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime which takes into account the magnitude of spiked eigenvalues sample size and dimensionality this regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues sample size and dimensionality play in principal component analysis our results are a natural extension of those in paul 2007 to a more general setting and solve the rates of convergence problems in shen et al 2013 they also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis and lead to a new covariance estimator for the approximate factor model called shrinkage principal orthogonal complement thresholding s poet that corrects the biases our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies

digitization scheme that assures faithful reconstruction of plane figures in the present extensive work we propose a digitization scheme for a broad class of plane figures it includes arbitrary polygons possibly non convex and with holes and plane sets whose boundary consists of smooth curves or straight segments our approach is based on an appropriate scaling of the original continuous real object so that the obtained magnified object and its appropriately constructed digitization feature analogous geometric properties as a bi product of the presented theory we prove the strong np hardness of the problem of obtaining an optimal i e with a minimal number of facets polyhedral reconstruction in which the facets are trapezoids or triangles this result implies the strong np hardness of the general polyhedral reconstruction problem which was a long standing open problem as another major result we show that the proposed digitization scheme allows faithful reconstruction of plane figures from the considered general class the reconstructed set features the basic properties of the original object such as location of curve and straight segments and inflection points of its boundary

simple and reliable estimators of coefficients of interest in a model with high dimensional confounding effects abstract often an investigator is interested in a single parameter or low dimensional parameter vector e g a treatment effect in a regression model rather than in the full set of regression coefficients there may also be a relatively high dimensional set of potential explanatory variables other than the effect of interest which if omitted could bias the estimate of the parameter of interest however there may be too many such variables to include all of them without substantial efficiency loss we suggest a simple easily computed estimator for this case using principal components to compute auxiliary regressors from the set of potential controls and establish the limit properties of the estimator allowing for dependence and heterogeneity as well as increasing dimension of the set of controls we also provide finite sample evidence on the performance of the estimator where principal components are selected in a one dimensional search using an appropriate information criterion as stopping rule for the number of components the results suggest that the estimator has practical usefulness in small samples

high dimensional covariance matrix estimation using a factor model abstract high dimensionality comparable to sample size is common in many statistical problems we examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to as the sample size n increases motivated by the arbitrage pricing theory in finance a multi factor model is employed to reduce dimensionality and to estimate the covariance matrix the factors are observable and the number of factors k is allowed to grow with p we investigate the impact of p and k on the performance of the model based covariance matrix estimator under mild assumptions we have established convergence rates and asymptotic normality of the model based estimator its performance is compared with that of the sample covariance matrix we identify situations under which the factor approach increases performance substantially or marginally the impacts of covariance matrix estimation on optimal portfolio allocation and portfolio risk assessment are studied the asymptotic results are supported by a thorough simulation study

projected principal component analysis in factor models this paper introduces a projected principal component analysis projected pca which employees principal component analysis to the projected smoothed data matrix onto a given linear space spanned by covariates when it applies to high dimensional factor analysis the projection removes noise components we show that the unobserved latent factors can be more accurately estimated than the conventional pca if the projection is genuine or more precisely when the factor loading matrices are related to the projected linear space when the dimensionality is large the factors can be estimated accurately even when the sample size is finite we propose a flexible semi parametric factor model which decomposes the factor loading matrix into the component that can be explained by subject specific covariates and the orthogonal residual component the covariates effects on the factor loadings are further modeled by the additive model via sieve approximations by using the newly proposed projected pca the rates of convergence of the smooth factor loading matrices are obtained which are much faster than those of the conventional factor analysis the convergence is achieved even when the sample size is finite and is particularly appealing in the high dimension low sample size situation this leads us to developing nonparametric tests on whether observed covariates have explaining powers on the loadings and whether they fully explain the loadings the proposed method is illustrated by both simulated data and the returns of the components of the s p 500 index

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

robust covariance estimation for approximate factor models in this paper we study robust covariance estimation under the approximate factor model with observed factors we propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors and then use it to recover the covariance matrix of the observed data we prove that once the initial matrix estimator is good enough to maintain the element wise optimal rate the whole procedure will generate an estimated covariance with desired properties for data with only bounded fourth moment we propose to use adaptive huber loss minimization to give the initial joint covariance estimation this approach is applicable to a much wider class of distributions beyond sub gaussian and elliptical distributions we also present an asymptotic result for adaptive huber s m estimator with a diverging parameter the conclusions are demonstrated by extensive simulations and real data analysis

parametric bootstrap and penalized quasi likelihood inference in conditional autoregressive models this paper discusses a variety of conditional autoregressive car models for mapping disease rates beyond the usual first order intrinsic car model we illustrate the utility and scope of such models for handling different types of data structures to encourage their routine use for map production at statistical and health agencies a simple algorithm for fitting such models is presented this is derived from penalized quasi likelihood pql inference which uses an analogue of best linear unbiased estimation for the regional risk ratios and restricted maximum likelihood for the variance components we offer the practitioner here the use of the parametric bootstrap for inference it is more reliable than standard maximum likelihood asymptotics for inference purposes since relevant hypotheses for the mapping of rates lie on the boundary of the parameter space we illustrate the parametric bootstrap test of the practically relevant and important simplifying hypothesis that there is no spatial autocorrelation although the parametric bootstrap requires computational effort it is straightforward to implement and offers a wealth of information relating to the estimators and their properties the proposed methodology is illustrated by analysing infant mortality in the province of british columbia in canada

distributed estimation of principal eigenspaces principal component analysis pca is fundamental to statistical machine learning it extracts latent principal factors that contribute to the most variation of the data when data are stored across multiple machines however communication cost can prohibit the computation of pca in a central location and distributed algorithms for pca are thus needed this paper proposes and studies a distributed pca algorithm each node machine computes the top k eigenvectors and transmits them to the central server the central server then aggregates the information from all the node machines and conducts a pca based on the aggregated information we investigate the bias and variance for the resulting distributed estimator of the top k eigenvectors in particular we show that for distributions with symmetric innovation the empirical top eigenspaces are unbiased and hence the distributed pca is unbiased we derive the rate of convergence for distributed pca estimators which depends explicitly on the effective rank of covariance eigen gap and the number of machines we show that when the number of machines is not unreasonably large the distributed pca performs as well as the whole sample pca even without full access of whole data the theoretical results are verified by an extensive simulation study we also extend our analysis to the heterogeneous case where the population covariance matrices are different across local machines but share similar top eigen structures

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

guarding a set of line segments in the plane we consider the following problem given a finite set of straight line segments in the plane find a set of points of minimum size so that every segment contains at least one point in the set this problem can be interpreted as looking for a minimum number of locations of policemen guards cameras or other sensors that can observe a network of streets corridors tunnels tubes etc we show that the problem is strongly np complete even for a set of segments with a cubic graph structure but in p for tree structures

hierarchical bayesian spatiotemporal analysis of revascularization odds using smoothing splines hierarchical bayesian models are proposed for over dispersed longitudinal spatially correlated binomial data this class of models accounts for correlation among regions by using random effects and allows a flexible modelling of spatiotemporal odds by using smoothing splines the aim is i to develop models which will identify temporal trends of odds and produce smoothed maps including regional effects ii to specify markov chain monte carlo mcmc inference for fitting such models iii to study the sensitivity of such bayesian binomial spline spatiotemporal analyses to prior assumptions and iv to compare mechanisms for assessing goodness of fit an analysis of regional variation for revascularization odds of patients hospitalized for acute coronary syndrome in quebec motivates and illustrates the methods developed

high dimensional minimum variance portfolio estimation under statistical factor models abstract we propose a high dimensional minimum variance portfolio estimator under statistical factor models and show that our estimated portfolio enjoys sharp risk consistency our approach relies on properly integrating l 1 constraint on portfolio weights with an appropriate covariance matrix estimator in terms of covariance matrix estimation we extend the theoretical results of poet fan et al 2013 to a setting that is coherent with principal component analysis simulation and extensive empirical studies on s p 100 index constituent stocks demonstrate favorable performance of our mvp estimator compared with benchmark portfolios

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

d cca a decomposition based canonical correlation analysis for high dimensional datasets a typical approach to the joint analysis of two high dimensional datasets is to decompose each data matrix into three parts a low rank common matrix that captures the shared information across dat

an optimal algorithm for solving the searchlight guarding problem on weighted interval graphs abstract in this paper a graph problem on connected weighted undirected graphs called the searchlight guarding problem is considered assume that there is a fugitive who moves along the edges of the graph at a random speed the task involves placing a set of searchlights at vertices to search the edges of the graph and to spot the fugitive suppose that placing a searchlight at some vertex incurs some building cost the searchlight guarding problem is to allocate a set s of searchlights at the vertices such that the total cost of the vertices in s is minimized if there is more than one set of searchlights each with a minimum building cost then identify the set with the minimum search time that is where the time slots needed to spot the fugitive is the minimum as is well established the problem is np hard on weighted bipartite graphs but is linear time solvable on weighted trees in this paper the design of a linear time optimal algorithm for the searchlight guarding problem on weighted interval graphs is presented it entails two phases in the first phase a set of searchlights with minimum guarding cost is identified and the search directions of all edges are assigned to achieve this task a new problem called the edge direction assignment problem is first defined and the problem on weighted complete split graphs is solved by the greedy strategy based on this computational result the problem of finding the set of searchlights with minimum guarding cost and assigning the search directions of all edges is solved by the dynamic programming strategy then in the second phase the search time slots of each edge are determined on the basis of the results of the first phase and on some properties of interval graphs

a randomized sequential procedure to determine the number of factors this paper proposes a procedure to estimate the number of common factors k in a static approximate factor model the building block of the analysis is the fact that the first k eigenvalues of the covariance matrix of the data diverge whilst the others stay bounded on the grounds of this we propose a test for the null that the i th eigenvalue diverges using a randomised test statistic based directly on the estimated eigenvalue the test only requires minimal assumptions on the data and no assumptions are required on factors loadings or idiosyncratic errors the randomised tests are then employed in a sequential procedure to determine k

estimation of a multiplicative covariance structure in the large dimensional case abstract we propose a kronecker product model for correlation or covariance matrices in the large dimensional case the number of parameters of the model increases logarithmically with the dimension of the matrix we propose a minimum distance md estimator based on a log linear property of the model as well as a one step estimator which is a one step approximation to the quasi maximum likelihood estimator qmle we establish rates of convergence and central limit theorems clt for our estimators in the large dimensional case a specification test and tools for kronecker product model selection and inference are provided in a monte carlo study where a kronecker product model is correctly specified our estimators exhibit superior performance in an empirical application to portfolio choice for s p500 daily returns we demonstrate that certain kronecker product models are good approximations to the general covariance matrix

principal component analysis of high frequency data we develop the necessary methodology to conduct principal component analysis at high frequency we construct estimators of realized eigenvalues eigenvectors and principal components and provide

asymptotic theory of eigenvectors for random matrices with diverging spikes characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications to this en

optimal shrinkage of eigenvalues in the spiked covariance model we show that in a common high dimensional covariance model the choice of loss function has a profound effect on optimal estimation in an asymptotic framework based on the spiked covariance model and use of orthogonally invariant estimators we show that optimal estimation of the population covariance matrix boils down to design of an optimal shrinker that acts elementwise on the sample eigenvalues indeed to each loss function there corresponds a unique admissible eigenvalue shrinker dominating all other shrinkers the shape of the optimal shrinker is determined by the choice of loss function and crucially by inconsistency of both eigenvalues and eigenvectors of the sample covariance matrix details of these phenomena and closed form formulas for the optimal eigenvalue shrinkers are worked out for a menagerie of 26 loss functions for covariance estimation found in the literature including the stein entropy divergence frechet bhattacharya matusita frobenius norm operator norm nuclear norm and condition number losses

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

optimal estimation and rank detection for sparse spiked covariance matrices this paper considers a sparse spiked covariance matrix model in the high dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection the optimal rate of convergence for estimating the spiked covariance matrix under the spectral norm is established which requires significantly different techniques from those for estimating other structured covariance matrices such as bandable or sparse covariance matrices we also establish the minimax rate under the spectral norm for estimating the principal subspace the primary object of interest in principal component analysis in addition the optimal rate for the rank detection boundary is obtained this result also resolves the gap in a recent paper by berthet and rigollet ann stat 41 4 1780 1815 2013 where the special case of rank one is considered

geometric representation of high dimension low sample size data summary high dimension low sample size data are emerging in various areas of science we find a common structure underlying many such data sets by using a non standard type of asymptotics the dimension tends to while the sample size is fixed our analysis shows a tendency for the data to lie deterministically at the vertices of a regular simplex essentially all the randomness in the data appears only as a random rotation of this simplex this geometric representation is used to obtain several new statistical insights

partitioning a polygonal region into trapezoids the problem of partitioning a polygonal region into a minimum number of trapezoids with two horizontal sides is discussed a triangle with a horizontal side is considered to be a trapezoid with two horizontal sides one of which is degenerate first a method of achieving a minimum partition is presented the number m of the trapezoids in the minimum partition of a polygonal region p is shown to be m n w h d 1 where n w and h are the number of vertices windows holes and horizontal edges of p respectively and d is the cardinality of a maximum independent set of the straight lines in the plane graph associated with p next this problem is shown to be polynomially equivalent to the problem of finding a maximum independent set of a straight lines in the plane graph and consequently it is shown to be np complete however for a polygonal region without windows an o n 2 time algorithm for partitioning it into a minimum number of trapezoids is presented finally an o n log n time approximation algorithm with the performance bound 3 is presented

estimation of large dimensional factor models with an unknown number of breaks abstract in this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time we propose a novel three step procedure to detect the breaks if any and then identify their locations in the first step we divide the whole time span into subintervals and fit a conventional factor model on each interval in the second step we apply the adaptive fused group lasso to identify intervals containing a break in the third step we devise a grid search method to estimate the location of the break on each identified interval we show that with probability approaching one our method can identify the correct number of changes and estimate the break locations simulation studies indicate superb finite sample performance of our method we apply our method to investigate stock and watson s 2009 u s monthly macroeconomic dataset and identify five breaks in the factor loadings spanning 1959 2006

the searchlight problem for road networks we consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines or two or more line segments in the plane some of the intersections of the road network are occupied by stationary guards equipped with a number of searchlights each of which can emit a single ray of light in any direction along the lines or line segments it is on the goal is to detect the intruder that is to illuminate its location guards may alter the direction in which they aim a searchlight but need to switch it off for some finite time interval to effect the change in contrast the intruder may move with arbitrary speed along the network but cannot pass guards and exploit this time interval to recontaminate previously illuminated sections of the network for various classes of road networks characterized by the number n of lines or line segments comprising it and the number g n 1 of possible locations of guards fixed in advance and guaranteed to give complete coverage we present several upper and lower bounds on the worst case number of searchlights each placed at one of the guard positions required to successfully search a given road network in particular we prove the following results 1 min 2 g 1 n 2 searchlights are sometimes necessary and min 7 3 g n 1 are always sufficient for searching a road network given as the union of n lines 2 g log n g searchlights are sometimes necessary and o g 2 log n searchlights are always sufficient for searching a road network given as the union of n line segments and3 at most one searchlight per guard position and hence a total of at most g searchlights is always sufficient for searching a road network given as the union of axis aligned lines or line segments the proofs of the upper bounds induce algorithms for generating a search schedule for detecting the intruder using the claimed number of searchlights the problem of searching for an intruder hiding in a road network is introduced upper and lower bounds on the worst case number of searchlights are presented the proofs of the upper bounds induce algorithms for generating a search schedule

inference in generalized additive mixed modelsby using smoothing splines generalized additive mixed models are proposed for overdispersed and correlated data which arise frequently in studies involving clustered hierarchical and spatial designs this class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression while accounting for correlation between observations by using random effects we estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi likelihood because numerical integration is often required by maximizing the objective functions double penalized quasi likelihood is proposed to make approximate inference frequentist and bayesian inferences are compared a key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software a bias correction procedure is also proposed to improve the performance of double penalized quasi likelihood for sparse data we illustrate the method with an application to infectious disease data and we evaluate its performance through simulation

generalized thresholding of large covariance matrices we propose a new class of generalized thresholding operators that combine thresholding with shrinkage and study generalized thresholding of the sample covariance matrix in high dimensions generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden we obtain an explicit convergence rate in the operator norm that shows the tradeoff between the sparsity of the true model dimension and the sample size and shows that generalized thresholding is consistent over a large class of models as long as the dimension p and the sample size n satisfy log p n 0 in addition we show that generalized thresholding has the sparsistency property meaning it estimates true zeros as zeros with probability tending to 1 and under an additional mild condition is sign consistent for nonzero elements we show that generalized thresholding covers as special cases hard and soft thresholding smoothly clipped absolute deviation and adaptive lasso and comp

functional car models for large spatially correlated functional datasets abstractwe develop a functional conditional autoregressive car model for spatially correlated data for which functions are collected on areal units of a lattice our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure in both the space and functional domains we show theoretically that our construction leads to a car model at each functional location with spatial covariance parameters varying and borrowing strength across the functional domain using basis transformation strategies the nonseparable spatial functional model is computationally scalable to enormous functional datasets generalizable to different basis functions and can be used on functions defined on higher dimensional domains such as images through simulation studies we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance applied to a high throughput spatiall

convergence and prediction of principal component scores in high dimensional settings a number of settings arise in which it is of interest to predict principal component pc scores for new observations using data from an initial sample in this paper we demonstrate that naive approaches to pc score prediction can be substantially biased towards 0 in the analysis of large matrices this phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase for the spiked eigenvalue model for random matrices we expand the generality of these results and propose bias adjusted pc score prediction in addition we compute the asymptotic correlation coefficient between pc scores from sample and population eigenvectors simulation and real data examples from the genetics literature show the improved bias and numerical properties of our estimators

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

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