Showing papers on "Covariance mapping published in 2001"

Nonparametric spatial covariance functions: Estimation and testing

Abstract: Spatial autocorrelation techniques are commonly used to describe genetic and ecological patterns. To improve statistical inference about spatial covariance, we propose a continuous nonparametric estimator of the covariance function in place of the spatial correlogram. The spline correlogram is an adaptation of a recent development in spatial statistics and is a generalization of the commonly used correlogram. We propose a bootstrap algorithm to erect a confidence envelope around the entire covariance function. The meaning of this envelope is discussed. Not all functions that can be drawn inside the envelope are candidate covariance functions, as they may not be positive semidefinite. However, covariance functions that do not fit, are not supported by the data. A direct estimate of the L0 spatial correlation length with associated confidence interval is offered and its interpretation is discussed. The spline correlogram is found to have high precision when applied to synthetic data. For illustration, the method is applied to electrophoretic data of an alpine grass (Poa alpina).

Analogies and correspondences between variograms and covariance functions

Abstract: Variograms and covariance functions are key tools in geostatistics. However, various properties, characterizations, and decomposition theorems have been established for covariance functions only. We present analogous results for variograms and explore the connections to covariance functions. Our _ndings include criteria for covariance functions on intervals, and we apply them to exponential models, fractional Brownian motion, and locally polynomial covariances. In particular, we characterize isotropic locally polynomial covariance functions of degree 3.

The Covariance Structure of Random Permutation Matrices

Abstract: Random permutation matrices (U) arise naturally in the stochas- tic representation of vectors of order statistics, induced order statistics and associated ranks. When the probability law of U is uniform, the covariance structure among the entries of U is derived explicitely, and a constructive derivation for the covariance in the general case (U k ) is described and related to the cyclic structure of the symmetric group. It is shown that the covari- ance structure of vectors resulting from the multiplicative action UX of U on a given vector X requires averaging the symmetric conjugates UXX 0 U 0 of XX' over the group of permutation matrices. The mean conjugate is a projection operator which leads to a trace decomposition with the usual ANOVA inter- pretation. Numerical examples of these decompositions are discussed in the context of the analysis of circularly symmetric data.

Influences of Different Additional Random Effects on Estimating Covariance Functions

Abstract: Growth records of 686 pigs of SD-Ⅱ Swine Line over 6 generations were used to study the influence of litter effect and animal effect,which was used as different additional random effect,on estimating additive genetic and permanent environmental covariance functionsA random regression model with Legendre polynomials of age as independent variables was used to estimate the covariance functions by restricted maximum likelihood employing the average information algorithm (AIREML)The results showed that litter effect only reflected part of the permanent environmental effects and full order fit was necessary to estimate the covariance functionsHowever,a reduced order fit was feasible using animal effect as additional random effectMoreover,it involved less parameters and smoothed out differences in estimates of the covariancesSignificance and application of covariance functions are discussed

Modeling 3-D anisotropic fractal media

Abstract: This paper presents stochastic descriptions of anisotropic fractal media. Second order statistics are used to represent the continuous random field as a stationary zero-mean process completely specified by its two-point covariance function. In analogy to the twodimensional Goff and Jordan model for seafloor morphology, I present the von Karman functions as a generalization to media with exponential correlation functions. I also compute a two-state model by mapping the random field from continuous realizations to a binary field. The method can find application in modeling impedances from fractal media and in fluid flow problems.

Estimation in a random effects model with parallel polynomial growth curves

Abstract: In this paper we consider an extended growth curve model with two hier- archical within-individuals design matrices, which is useful in analyzing mean profiles of several groups with parallel polynomial growth curves. The covariance structure based on a random eects model is assumed. The maximum likelihood estimators (MLE's) are obtained under the random eects covariance structure. The e‰ciency of the MLE is discussed. A numerical example is also given.

Covariance and Correlation Coefficient of Complex Random Variables

Abstract: Several properties of covariance and correlation coefficient of complex random variables are discussedThe necessary and sufficient condition of linear correlation between two complex random variables is established thereby

Exact distribution of the mle of concentration matrices in decomposable covariance selection models

Abstract: Covariance selection models were introduced by Dempster (1972). The covariance selection model with a decomposable graph is called a decomposable covariance selection model. Based on the hyper-Markov property (Dawid and Lau- ritzen (1993)), the exact distribution of the Maximum Likelihood Estimator (MLE) of the concentration matrix in the decomposable covariance selection model is given.