Showing papers on "Covariance mapping published in 1978"

Probabilities of Non-Positive Definite between-Group or Genetic Covariance Matrices

Abstract: The probability (Q) that the estimated between-group covariance matrix is not positive deJinite is computed for the balanced single classlfication multivariate analysis of variance with random effects. It is shown that Q depends only on the roots of the matrix product of the inverse of the true within-group and the true between-group covariance matrices which, for independent variables, reduces to expressions in intra-class correlations. Values of Q are computedfor ranges of size of experiment, intra-class correlation and number of variables. Even for large experiments, Q can approach 100% if there are many variables, for example with 160 groups of size 10 and either 8 independent variables each with intra-class 0.025 or 14 variables each with intra-class correlation 0.0625. Some rationalization of the results is given in terms of the bias in the roots of the sample between-group covariance matrix. In genetic applications, the between-group covariance matrix is proportional to the genetic covariance matrix, if non-positive definite, heritabilities and ordinary or partial genetic correlations are outside their valid limits, and the effiect on selection index construction is discussed.

A simple comprehensive model for the analysis of covariance structures

Abstract: A model is described which contains as special cases a large number of models for the analysis of covariance structures. Using rules for a calculus of functions of matrices given by McDonald & Swaminathan (1973), the first and second derivatives are given, for any loss function, with respect to the parameters of the hypothesis, thus enabling a variety of methods of fitting and testing it.

Analytical studies on some statistical properties of mean values and their applications to sampling in one dimension

Abstract: This paper documents the results of investigations on the variance and covariance properties of mean values within the theory of stationary random functions under a variety of conditions. Analytical expressions have been developed in each case, to facilitate direct and ready applications of the results, using the exponential function as a working model for the covariance function. These properties, in turn, have been utilized in developing mathematical expressions for estimation accuracy (error variance) of the mean estimates for one-dimensional sampling plans. Two distinctly different sampling plans have been discussed: “punctual” sampling with no significant linear extensions of the samples and “linear” sampling with significant linear extensions of samples in the direction of the section being sampled.

The random capacitance equation

Abstract: The initial value problem for a circuit containing a small random capacitance is studied. The randomly varying capacitance is taken to be zero-mean, gaussian processes with prescribed covariance function. The method of first-order smoothing is employed to determine the mean solution. Explicit results are shown for a negative exponential correlation function. The covariance of the solution is also obtained in the form of a double integral over the Green's function and the mean of the solution.