Diagnostic tests for the distribution of random effects in multivariate mixed effects models

Abstract

Fourier methods are proposed for testing the distribution of random effects in classical and robust multivariate mixed effects models. The test statistics involve estimation of the characteristic function of random effects. Theoretical and computational issues are addressed while Monte Carlo results show that the new procedures compare favorably with other methods.     

Estimating the order of moving average models: the max X2 method

The max X² technique for estimating rhe order of autoregressive processes (McClave (1976)) is extended to moving average models. The autöregressive-moving average duality is exploited by using the inverse autocorrelation function and the subset autoregression algorithm. The technique is demonstrated via simulations, and is applied to Box and Jenkins (1970) Series A.     

Sample-size requirements for confidence bounds of prescribed precision on multivariate normal quantiles

The problem of setting confidence bounds on a central multivariate normal quantile is considered. It is shown that for the setting of exact confidence bounds of specified closeness to the quantile,the required minimum size of a normal sample is large and rises rapidly with the number of variates considered.     

A test for bivariate symmetry based on the empirical distribution function

Hollander (1970) proposed a conditionally distribution-free test of bivariate symmetry based on the empirical distribution function. In this paper Hollander’s test statistic is examined In greater detail: in particular; its conditional asymptotic distribution is derived under the null hypothesis as well as under a sequence of local alternatives. Percentage points of the asymptotic distribution are presented; a power comparison between Hollander’s statistic and the likelihood ratio criterion in testing a variant of the sphericity hypothesis in multivariate analysis is made.     

Minimax property of stein's estimator

Stein's estimator and some other estimators of the mean of a K-variate normal distribution are known to dominate the maximum likelihood estimator under quadratic loss for K > 3, and are therefore minimax. In this paper it is shown that the minimax property of Stein's rule is preserved with respect to a generalized loss function.     

Maximum likelihood estimation of variance components in a completely random bib design

ABSTRACT

The purposes of this paper are to abstract from a number of articles variance component estimation procedures which can be used for completely random balanced incomplete block designs, to develop an iterated least squares (ITLS) computing algorithm for calculating maximum likelihood estimates, and to compare these procedures by use of simulated experiments. Based on the simulated experiments, the estimated mean square errors of the ITLS estimates are generally less than*those for previously proposed analysis of variance and symmetric sums estimators.     

A probabilistic model for predicting total basal area growth of closed uneven-aged stand

In this note, a probabilistic method for predicting the future total net basal area of closed uneven-aged stand based on “Stand Tally” is proposed and an example is given.     

Cramér-Rao lower bounds for estimators based on censored data

The Cramér-Rao lower bounds for the variances of unbiased estimators based on censored data are given. Useful techniques of evaluation are then derived for these lower bounds. Examples are given to illustrate these techniques. Small-sample comparisons are made between the resulting lower bounds, the variances of the best linear unbiased estimators, and the variances of unbiased esti-mators which are based on the maximum likelihood estimators.     

Pseudo-bayes estimation of multinomial proportions

In the simultaneous estimation of multinomial proportions, two estimators are developed which incorporate prior means and a prior parameter which reflects the accuracy of the prior means. These estimators possess substantially smaller risk than the standard estimator in a region of the parameter space and are much more robust than the conjugate Bayes estimator with respect to parameter values far from the prior mean. When vague prior information is available, these estimators and confidence regions derived from them appear to be attractive alternatives to the procedures based on the standard estimator.     

Tests for symmetry about an unknown value based on the empirical distribution function

A class of Kolmogorov-Smirnov and Cramér-von Mises type statistics for testing symmetry about an unknown value is described. These statistics are not distribution-free, however, and, indeed, are not readily amenable to calculation. A linear rank statistic analog of the first component of the Cramér-von Mises type statistic is investigated. Asymptotic non-null properties of these procedures in the normal case are studied, and an efficiency comparison of the Cramér-vonMises statistic, the linear rank statistic analog, the modified Wil-coxon statistic, and the likelihood ratio test is reported.