amge coarsening strategies and application to the oseen equations we provide some extensions to the algebraic multigrid method based on element interpolation amge concerning the agglomeration process the application to nonconforming elements and the application to the mixed finite element discretization of the oseen linearized navier stokes equations this last point using amge for mixed finite elements becomes straightforward because of the availability of coarse level topologies we show this exemplarily for the crouzeix raviart element including a stability result the numerical results show that it really pays off to take a closer look at the agglomeration strategy a wrong choice can lead to insufficient convergence or even divergence of the overall multigrid method

asymptotic distributions of quasi maximum likelihood estimators for spatial autoregressive models this paper investigates asymptotic properties of the maximum likelihood estimator and the quasi maximum likelihood estimator for the spatial autoregressive model the rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model it is important to make the distinction with dif ferent spatial scenarios under the scenario that each unit will be influenced by only a few neighboring units the estimators may have n rate of convergence and be asymp totically normal when each unit can be influenced by many neighbors irregularity of the information matrix may occur and various components of the estimators may have different rates of convergence

spatial prediction of soil salinity using electromagnetic induction techniques 1 statistical prediction models a comparison of multiple linear regression and cokriging we describe a regression based statistical methodology suitable for predicting field scale spatial salinity ec conditions from rapidly acquired electromagnetic induction ec data this technique uses multiple linear regression mlr models to estimate soil salinity from ec survey data the mlr models incorporate multiple ec measurements and trend surface parameters to increase the prediction accuracy and can be fitted from limited amounts of ec calibration data this estimation technique is compared to some commonly recommended cokriging techniques with respect to statistical modeling assumptions calibration sample size requirements and prediction capabilities we show that mlr models are theoretically equivalent to and cost effective relative to cokriging for estimating a spatially distributed random variable when the residuals from the regression model are spatially uncorrelated mlr modeling and prediction techniques are demonstrated with data from three salinity surveys

decorrelation property of discrete wavelet transform under fixed domain asymptotics theoretical aspects of the decorrelation property of the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing domain perspective in which the distance between neighboring observations stays roughly constant as the number of observations increases to understand the underlying data generating process and to obtain good interpolations fixed domain asymptotics in which the number of observations increases in a fixed region is often more appropriate than increasing domain asymptotics in the fixed domain setting we prove that for a general class of inhomogeneous covariance functions with suitable choice of wavelet filters the wavelet transform of a nonstationary process has mostly asymptotically uncorrelated components

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

fitting continuous arma models to unequally spaced spatial data abstract methods for fitting continuous spatial autoregressive moving average arma models to unequally spaced observations in two dimensions are reviewed and extended these are models with rational two dimensional spectra assuming gaussian input noise and observational errors maximum likelihood methods are used to estimate the arma parameters and the regression coefficients of the deterministic trend when the number of observations is too large for exact maximum likelihood estimation approximate maximum likelihood estimation is used based on nearest neighbors comparisons of nearest neighbor methods with exact likelihood methods are presented predictions of the height of the field at unobserved points can be calculated with confidence intervals

spectral methods for nonstationary spatial processes summary we propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process we also study the asymptotic properties of the proposed estimators via shrinking asymptotics assuming the distance between neighbouring observations tends to zero as the size of the observation region grows without bound with this type of asymptotic model we can uniquely determine the spectral density avoiding the aliasing problem we also present a new class of nonstationary processes based on a convolution of local stationary processes this model has the advantage that the model is simultaneously defined everywhere unlike moving window approaches but it retains the attractive property that locally in small regions it behaves like a stationary spatial process applications include the spatial analysis and modelling of air pollution data provided by the us environmental protection agency

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

covariance tapering for likelihood based estimation in large spatial data sets maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on gaussian processes but calculating the likelihood can be computationally infeasible for large data sets requiring o n3 calculations for a data set with n observations this article proposes the method of covariance tapering to approximate the likelihood in this setting in this approach covariance matrixes are tapered or multiplied element wise by a sparse correlation matrix the resulting matrixes can then be manipulated using efficient sparse matrix algorithms we propose two approximations to the gaussian likelihood using tapering one of these approximations simply replaces the model covariance with a tapered version whereas the other is motivated by the theory of unbiased estimating equations focusing on the particular case of the matern class of covariance functions we give conditions under which estimators maximizing the tapering approximations are like the maximum likelihood estimat

asymptotic theory of cepstral random fields random fields play a central role in the analysis of spatially correlated data and as a result have a significant impact on a broad array of scientific applications given the importance of this topic there has been a substantial amount of research devoted to this area however the cepstral random field model remains largely underdeveloped outside the engineering literature we provide a comprehensive treatment of the asymptotic theory for two dimensional random field models in particular we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving average random field which facilitates easy computation of the necessary autocovariance matrix additionally we establish asymptotic consistency results for bayesian maximum likelihood and quasi maximum likelihood estimation of random field parameters and regression parameters further in both the maximum and quasi maximum likelihood frameworks we derive the asymptotic distribution of our estimator the theoretical results are presented generally and are of independent interest pertaining to a wide class of random field models the results for the cepstral model facilitate model building because the cepstral coefficients are unconstrained in practice numerical optimization is greatly simplified and we are always guaranteed a positive definite covariance matrix we show that inference for individual coefficients is possible and one can refine models in a disciplined manner finally our results are illustrated through simulation and the analysis of straw yield data in an agricultural field experiment

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

modality of the restricted likelihood for spatial gaussian random fields summary numerical simulations recently reported in the literature have shown that the profile likelihood associated with the estimation of covariance range parameters for a gaussian field can be multimodal here we complement these recent results by considering covariances with unknown nugget scale and range parameters estimation is performed in a restricted maximum likelihood framework for unbounded sampling domains and known range parameter conditions ensuring asymptotic unimodality of the restricted likelihood are derived for bounded sampling domains monte carlo simulations indicate that if the range parameter is known multimodality is relatively rare unless the sample size is small for unknown range parameter frequencies of multimodality can be large and may increase with the sample size for the gaussian and spherical covariance models

prediction and creation of smooth curves for temporally correlated longitudinal data abstract this article presents a method of obtaining smoothed curves for a sample of individuals that permits an arbitrary number and spacing of observations for each individual we consider the case where each individual s curve cannot be separately estimated because either the n i s are too small or no suitable parametric forms for the random effects are available the model assumes a parametric form for the population mean curve and the correlation of the repeated measures the assumed correlation structure is evaluated using the empirical semivariogram a function of the sum of the squared differences of within individual residuals a method is proposed to validate the form and stationarity of the correlation structure maximum likelihood estimates for the population mean parameters and variance components are obtained simultaneously these estimates may be used to create a semiparametric differentiable curve and to predict future values for each individual using a method called kriging this method

on multimodality of the likelihood in the spatial linear model summary a popular covariance scheme used for the spatial linear model in geostatistics has spherical form however the likelihood is not twice differentiable with respect to the range parameter and this raises some questions regarding the unimodality of the likelihood we compare the likelihoods of the spatial linear model for small samples under this scheme and the doubly geometric scheme also a power covariance with range parameter is proposed in view of potential multimodal likelihoods for small samples for this model a convenient profile likelihood is introduced and studied

partitioned solution algorithms for fluid structure interaction problems with hyperelastic models in this work we consider fluid structure interaction simulation with nonlinear hyperelastic models in the solid part we use a partitioned approach to deal with the coupled nonlinear fluid structure interaction problems we focus on handling the nonlinearity of the fluid and structure sub problems using adaptive newton s method the near incompressibility of materials the stabilization of employed finite element discretization and the robustness and efficiency of krylov subspace and algebraic multigrid methods for the linearized algebraic equations

minimum norm quadratic estimation of spatial variograms abstract the estimation of spatial variograms a measure of spatial correlation is a critical problem in the implementation of kriging a method for interpolating random fields we consider the use of minimum norm quadratic estimators of the variogram when it is specified up to a finite number of linear parameters we investigate the asymptotic behavior of such estimators for gaussian processes as the number of observations within some bounded region increases the basic conclusion is that we can estimate consistently those functions of the parameters and only those functions that have a nonnegligible impact asymptotically on the kriging procedure in general the behavior of the variogram over relatively short distances is the only aspect of the variogram that is asymptotically important as an example consider a gaussian process z on the real line with unknown constant mean and where is known as the semivariogram of the process and is a finite vector of unknown parameters suppose for 0

an incomplete data approach to the analysis of covariance structures in this paper linear structural equation models with latent variables are considered it is shown how many common models arise from incomplete observation of a relatively simple system subclasses of models with conditional independence interpretations are also discussed using an incomplete data point of view the relationships between the incomplete and complete data likelihoods assuming normality are highlighted for computing maximum likelihood estimates the em algorithm and alternatives are surveyed for the alternative algorithms simplified expressions for computing function values and derivatives are given likelihood ratio tests based on complete and incomplete data are related and an example on using their relationship to improve the fit of a model is given

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

optimal geostatistical model selection in many fields of science predicting variables of interest over a study region based on noisy data observed at some locations is an important problem two popular methods for the problem are kriging and smoothing splines the former assumes that the underlying process is stochastic whereas the latter assumes it is purely deterministic kriging performs better than smoothing splines in some situations but is outperformed by smoothing splines in others however little is known regarding selecting between kriging and smoothing splines in addition how to perform variable selection in a geostatistical model has not been well studied in this article we propose a general methodology for selecting among arbitrary spatial prediction methods based on approximately unbiased estimation of mean squared prediction errors using a data perturbation technique the proposed method accounts for estimation uncertainty in both kriging and smoothing spline predictors and is shown to be optimal in terms of two mean sq

a linear spatial correlation model with applications to positron emission tomography abstract a simple spatial correlation model is presented for repeated measures data correlation between observations on the same subject is assumed to decay as a linear function of the squared distance separating the regions in three dimensional space where the observations are made this quadratic decay qd model has many attractive theoretical properties the covariance structure of the normalized data formed by subtracting the subject average is the same as that generated by random linear trends plus centered white noise which leads to a simple method for simulating the original data it also implies that the first three principal components of the normalized observations are the spatial coordinates of the regions thus principal components analysis can be used as an exploratory tool to verify the qd model provided the white noise component is small certain simple predictions can be made such as the fact that the variances of the normalized observations increase linearly with the squared dist

the method of normalized correlations a fast parameter estimation method for random processes and isotropic random fields that focuses on short range dependence we focus on the inference of covariance parameters from spatial or temporal data using the method of normalized correlations monc we compare the monc with maximum likelihood estimation and weighted least squares using simulated data as well as gridded and scattered real data for the synthetic experiments none of the methods considered performed uniformly better than the others in terms of estimation accuracy and precision however for regularly spaced data the monc was significantly faster and practically insensitive to sample size for scattered data the monc s speed was reduced but still competitive potential applications of the monc include those involving large data sets and fast preconditioning

assessing the significance of the correlation between two spatial processes modified tests of association based on the correlation coefficient or the covariance between two spatially autocorrelated processes are presented these tests can be used both for lattice and nonlattice data they are based on the evaluation of an effective sample size that takes into account the spatial structure for positively autocorrelated processes the effective sample size is reduced a method for evaluating this reduction via an approximation of the variance of the correlation coefficient is developed the performance of the tests is assessed by monte carlo simulations the method is illustrated by examples from geographical epidemiology

approximating likelihoods for large spatial data sets summary likelihood methods are often difficult to use with large irregularly sited spatial data sets owing to the computational burden even for gaussian models exact calculations of the likelihood for n observations require o n3 operations since any joint density can be written as a product of conditional densities based on some ordering of the observations one way to lessen the computations is to condition on only some of the past observations when computing the conditional densities we show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating through theoretical numerical and practical examples we show that there can often be considerable benefit in conditioning on some distant observations as well

fixed domain asymptotic properties of tapered maximum likelihood estimators when the spatial sample size is extremely large which occurs in many environmental and ecological studies operations on the large covariance matrix are a numerical challenge covariance tapering is a technique to alleviate the numerical challenges under the assumption that data are collected along a line in a bounded region we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator mle for the microergodic parameter in the matern covariance function by establishing the fixed domain asymptotic distribution of the exact mle and that of the tapered mle our results imply that under some conditions on the taper the tapered mle is asymptotically as efficient as the true mle for the microergodic parameter in the matern model

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

the role of the range parameter for estimation and prediction in geostatistics summary two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations we show that asymptotic results for a gaussian process over a fixed domain with mat ern covariance function previously proven only in the case of a fixed range parameter can be extended to the case of jointly estimating the range and the variance of the process moreover we show that intuition and approximations derived from asymptotics using a fixed range parameter can be problematic when applied to finite samples even for large sample sizes in contrast we show via simulation that performance is improved and asymptotic approximations are applicable for smaller sample sizes when the parameters are jointly estimated these effects are particularly apparent when the process is mean square differentiable or the effective range of spatial correlation is small

estimation and model identification for continuous spatial processes summary formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced the processes are assumed to be adequately described by a linear model with residuals that follow a second order stationary gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations a general class of two dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function an iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non lattice data the procedure is applied to several generated data sets and to an actual ground water data set

an algebraic multigrid method for linear elasticity we present an algebraic multigrid amg method for the efficient solution of linear block systems stemming from a discretization of a system of partial differential equations pdes it generalizes the classical amg approach for scalar problems to systems of pdes in a natural blockwise fashion we apply this approach to linear elasticity and show that the block interpolation described in this paper reproduces the rigid body modes i e the kernel elements of the discrete linear elasticity operator it is well known from geometric multigrid methods that this reproduction of the kernel elements is an essential property to obtain convergence rates which are independent of the problem size we furthermore present results of various numerical experiments in two and three dimensions they confirm that the method is robust with respect to variations of the poisson ratio nu we obtain rates rho 0 4 for nu 0 4 these measured rates clearly show that the method provides fast convergence for a large variety of discretized elasticity problems

stabilized finite element methods for the generalized oseen problem the numerical solution of the non stationary incompressible navierstokes model can be split into linearized auxiliary problems of oseen type we present in a unique way different stabilization techniques of finite element schemes on isotropic meshes first we describe the state of the art for the classical residual based supg pspg method then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method these methods are closely related to the concept of variational multiscale methods which seems to provide a new approach to large eddy simulation finally we give a critical comparison of these methods

an approximate method of evaluating the joint likelihood for first order gmrfs a highly accurate approximation is proposed for computing the joint likelihood for first order gauss markov random fields gmrfs defined on irregularly shaped lattices the problem in computing the likelihood lies in evaluating the determinant of a very large matrix b its exact evaluation is limited to either very small irregular regions or a few regularly shaped regions the approximation proposed here is based on an eigenanalysis of b

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

an asymptotic approximation to the n mixture model for the estimation of disease prevalence n mixture models are probability models that estimate abundance using replicate observed counts while accounting for imperfect detection in this article we propose an asymptotic approximation to the n mixture model which efficiently estimates large abundances without the computational limitations of the generalized n mixture model introduced by dail and madsen in 2011 it has been suggested in the literature that n mixture models do not perform well when counts from the same sites show weak patterns of population dynamics our proposed model addresses this issue by using the asymptotic information matrix to diagnose model parameter estimability and to derive parameter standard errors a simulation study show that this model performs almost as well as the dail madsen generalized n mixture model at low abundances and improves on it at higher abundances we illustrate the procedure using two data sets the american robin data from dail and madsen 2011 and counts of chlamydia cases in the state of oregon from 2007 2016 the chlamydia data exhibit very large abundances and demonstrate the potential usefulness of the proposed model for disease surveillance data

asymptotic theory with hierarchical autocorrelation ornstein uhlenbeck tree models hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree the residual covariance is parametrized using the tree distance between sampling units when observations are modeled using an ornstein uhlenbeck ou process along the tree the autocorrelation between two tips decreases exponentially with their tree distance these models are most often applied in evolutionary biology when tips represent biological species and the ou process parameters represent the strength and direction of natural selection for these models we show that the mean is not microergodic no estimator can ever be consistent for this parameter and provide a lower bound for the variance of its mle for covariance parameters we give a general sufficient condition ensuring microergodicity this condition suggests that some parameters may not be estimated at the same rate as others we show that indeed maximum likelihood estimators of the autocorrelation parameter converge at a slower rate than that of generally microergodic parameters we showed this theoretically in a symmetric tree asymptotic framework and through simulations on a large real tree comprising 4507 mammal species

numerical simulation of fluid structure interaction problems on hybrid meshes with algebraic multigrid methods fluid structure interaction problems arise in many fields of application such as flows around elastic structures and blood flow in arteries the method presented in this paper for solving such a problem is based on a reduction to an equation at the interface involving the so called steklov poincare operators this interface equation is solved by a newton iteration for which directional derivatives involving shape derivatives with respect to the interface perturbation have to be evaluated appropriately one step of the newton iteration requires the solution of several decoupled linear sub problems in the structure and the fluid domains these sub problems are spatially discretized by a finite element method on hybrid meshes for the time discretization implicit first order methods are used for both sub problems the discretized equations are solved by algebraic multigrid methods

bayesian segmentation via asymptotic partition functions asymptotic approximations to the partition function of gaussian random fields are derived textures are characterized via gaussian random fields induced by stochastic difference equations determined by finitely supported stationary linear difference operators adjusted to be nonstationary at the boundaries it is shown that as the scale of the underlying shape increases the log normalizer converges to the integral of the log spectrum of the operator inducing the random field fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator induced random field model matrix analysis techniques are proposed for handling textures with variable orientation examples of texture parameters estimated from training data via asymptotic maximum likelihood are shown isotropic models involving powers of the laplacian and directional models involving partial derivative mixtures are explored parameters are estimated for mitochondria and actin myocin complexes in electron micrographs and clutter in forward looking infrared images deformable template models are used to infer the shape of mitochondria in electron micrographs with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds

multi task sparse structure learning with gaussian copula models multi task learning mtl aims to improve generalization performance by learning multiple related tasks simultaneously while sometimes the underlying task relationship structure is known often the structure needs to be estimated from data at hand in this paper we present a novel family of models for mtl applicable to regression and classification problems capable of learning the structure of tasks relationship in particular we consider a joint estimation problem of the tasks relationship structure and the individual task parameters which is solved using alternating minimization the task relationship revealed by structure learning is founded on recent advances in gaussian graphical models endowed with sparse estimators of the precision inverse covariance matrix an extension to include exible gaussian copula models that relaxes the gaussian marginal assumption is also proposed we illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classification we also consider the problem of combining earth system model esm outputs for better projections of future climate with focus on projections of temperature by combining esms in south and north america and show that the proposed model outperforms several existing methods for the problem

a new method of prediction for spatial regression models with correlated errors summary this paper deals with minimum mean squared error unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations the process is assumed to be governed by a linear regression model with errors that follow a second order stationary gaussian random field a new method of prediction is developed that is compatible with the parameter estimation procedures of vecchia the result is a new likelihood based method for joint parameter estimation and prediction that can be applied to large or small data sets with irregularly spaced data simulated and observed data sets are analysed to illustrate the methods

a resampling based stochastic approximation method for analysis of large geostatistical data the gaussian geostatistical model has been widely used in modeling of spatial data however it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix particularly when there is a large number of observations this article proposes a resampling based stochastic approximation method to address this challenge at each iteration of the proposed method a small subsample is drawn from the full dataset and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation since the proposed method makes use of only a small proportion of the data at each iteration it avoids inverting large covariance matrices and thus is scalable to large datasets the proposed method also leads to a general parameter estimation approach maximum mean log likelihood estimation which includes the popular maximum log likelihood estimation mle approach as a special case and is expected to play an important role

on the unbiasedness of the papadakis estimator and other nonlinear estimators of treatment contrasts in field plot experiments summary spatial methods for the analysis of field plot experiments are considered estimators of treatment contrasts obtained by these methods are generally complicated nonlinear functions of the observations sufficient conditions for these estimators to be unbiased under a postulated true model are obtained the analysis of data from field plot experiments or other spatial experiments generally includes the estimation of treatment contrasts a common approach to their estimation is to apply ordinary least squares to a linear model in which the expected value of each observation is taken to be the sum of an overall mean a treatment effect and various environmental effects such as block or row and column effects this approach yields estimators which are linear functions of the observations and which are unbiased if the assumed model is correct recently numerous spatial methods for the analysis of data from field plot experi ments have been proposed see for example bartlett 1978 wilkinson et al 1983 besag kempton 1986 williams 1986 and gleeson cullis 1987 these alternatives to a traditional least squares analysis attempt to neutralize the disruptive effect that the spatial heterogeneity of the experimental units can have on the estimation of treatment contrasts randomization studies of uniformity trial data conducted by besag kempton 1986 indicate that spatial methods yield estimators of treatments contrasts which in the presence of appreciable spatial heterogeneity are likely to be more efficient than traditional estimators however because the estimators produced by spatial methods are complicated nonlinear functions of the observations little else is known about their properties in what follows we give conditions under which these estimators are unbiased under a postulated true model

comparing spatial predictions under a general loss function we develop a hypothesis test to determine whether a significant difference in the spatial predictions produced by two competing models exists on average across the entire spatial domain of interest the null hypothesis is that of no difference and a spatial loss differential is created based on the observed data the two sets of predictions and the loss function chosen by the researcher the test assumes only isotropy and short range spatial dependence of the loss differential but does allow it to be non gaussian non zero mean and spatially correlated constant and nonconstant spatial trends in the loss differential are treated in two separate cases monte carlo simulations illustrate the size and power properties of this test and an example based on daily average wind speeds in oklahoma is used for illustration supplemental results are available online

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

large panels with common factors and spatial correlation this paper considers the statistical analysis of large panel data sets where even after condi tioning on common observed eects the cross section units might remain dependently distrib uted this could arise when the cross section units are subject to unobserved common eects and or if there are spill over eects due to spatial or other forms of local dependencies the paper provides an overview of the literature on cross section dependence introduces the con cepts of time speci c weak and strong cross section dependence and shows that the commonly used spatial models are examples of weak cross section dependence it is then established that the common correlated eects cce estimator of panel data model with a multifactor error structure recently advanced by pesaran 2006 continues to provide consistent estimates of the slope coe cient even in the presence of spatial error processes small sample properties of the cce estimator under various patterns of cross section dependence including spatial forms are investigated by monte carlo experiments results show that the cce approach works well in the presence of weak and or strong cross sectionally correlated errors we also explore the role of certain characteristics of spatial processes in determining the performance of cce estimators such as the form and intensity of spatial dependence and the sparseness of the spatial weight

tukey g and h random fields abstractwe propose a new class of transgaussian random fields named tukey g and h tgh random fields to model non gaussian spatial data the proposed tgh random fields have extremely flexible marginal distributions possibly skewed and or heavy tailed and therefore have a wide range of applications the special formulation of the tgh random field enables an automatic search for the most suitable transformation for the dataset of interest while estimating model parameters asymptotic properties of the maximum likelihood estimator and the probabilistic properties of the tgh random fields are investigated an efficient estimation procedure based on maximum approximated likelihood is proposed and an extreme spatial outlier detection algorithm is formulated kriging and probabilistic prediction with tgh random fields are developed along with prediction confidence intervals the predictive performance of tgh random fields is demonstrated through extensive simulation studies and an application to a dataset

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

a comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors predicting values of a spatially distributed variable such as the concentration of a mineral throughout an ore body or the level of contamination around a toxic waste dump can be accomplished by a regression procedure known as kriging kriging and other types of statistical inference for spatially distributed variables are based on models of stochastic processes y t t d called random field models a commonly used class of random field models are the intrinsic models for which the mean is constant and half of the variance of yt ys is a function called the semivariogram of the difference t s the type of kriging corresponding to an intrinsic model is called ordinary kriging the semivariogram which typically is taken to depend on one or more unknown parameters must be estimated prior to ordinary kriging various estimators of the semivariogram s parameters have been proposed for two gaussian intrinsic random field models we compare by a monte carlo simulation study the performance o