Bayesian approach to estimation of intraclass correlation using reference prior

For the balanced variance component model when the intraclass correlation coefficient is of interest, Bayesian analysis is often appropriate. Berger and Bernardo’s (1992a) grouped ordering reference prior approach is used to analyze this model. The reference priors are developed and compared for the posterior inference with real and simulated data. We examine whether the reference priors satisfy the probability-matching criterion. Further, the reference prior is shown to be good in the sense of correct frequentist coverage probability of the posterior quantile.     

Extreme probabilities for contingency tables under row and column independence with application to fisher's exact test

Theorerms are proved for the maxima and minima of IIR_i!/IIC_j!/T!II_yij ! over r× c contingcncy tables Y=(y_ij) with row sums R₁,…,R_r, column sums C₁,…,C_c, and grand total T. These results are imlplemented into the network algorithm of Mehta and Patel (1983) for computing the P-value of Fisher's exact test for unordered r×c contingency tables. The decrease in the amount of computing time can be substantial when the column sums are very different.     

Covariate classification by post–stratification

The plug–in Anderson's covariate classification statistic is constructed on the basis of an initially unclassified training sample by means of posty–stratification. The asymptotic efficiency relative to the discriminant based on an initially classified training sample is evaluated for the case where a covariate is present. Effect of post–stratification is examined.     

The power functions of the likelihood ratio tests for a simply ordered trend in normal means

Likelihood ratio tests for the homogeneity of k normal means with the alternative restricted by an increasing trend are considered as well as the likelihood ratio tests of the null hypothesis that the means satisfy the trend. While the work is primarily a survey of results concerning the power functions of these tests, the extensions of some results to the case of not necessarily equal sample sizes are presented. For the case of known or unknown population variances, exact expressions are given for the power functions for k=3,4, and approximations are discussed for larger k. The topics of consistency, bias and monotonicity of the power functions are included. Also, Bartholomew's conjectures concerning minimal and maximal powers are investigated, with results of a new numerical study given.     

A modification of watson's statistic for goodness-of-fit

A modification of Watson's statistic is suggested for dealing with stochastically ordered alternatives in the goodness-of-fit setting.     

An extension of the median test to analysis of variance

In a k-way analysis of variance model, the major concern is testing for main effects and for the presence of interaction between the factors. When the assumptions of normality and equal variances are satisfied, the appropriate test to use is the usual F-test for ANOVA. However, when the normality assumption is not satisfied then a robust or nonparametric test is needed to conduct the analysis. In this paper a nonparametric method based on cell counts is proposed. Each cell is divided into L subcells based on predetermined outpoints and the resulting frequencies are laid out in a contingency table. Then the Pearson x² and tne likelihood ratio tests are performed. A comparison with the classical ANOVA F-test indicates that the proposed method is preferable when the data comes from a thick-tailed highly skewed distribution.     

Cumulants of random sum distributions

Consider a random variable S being the sum of a number N of independent and identically distributed random variables X_j (j = 1, 2, ...) where the number N is itself a non-negative integer-valued random variable independent of the X_j An explicit expression of the r-th cumulant of S is given in terms of the cumulants of N and X_j, Asymptotic properties of the distribution of S are also discussed.     

A class of distribution-free tests for two-way layout

In this article a class of distribution-free tests for the hypothesis of no row (treatment) effect in a two-way layout design, with several observations per cell, is proposed. The tests are based on U-statistics, constructed by considering minima of all possible subsamples of same size from each cell.The proposed class of tests is compared with the parametric test, Mack and Skillings test and Yate's test for two-way layout, in terms of Pitman ARE sense. It is seen that for the case of equal number of observations per cell, the proposed tests have better efficiency for exponential and uniform error distributions.     

Quadratic perturbation expansions of certain functions of eigenvalues and eigenvectors and their application to sensitivity analysis in multivariate methods

Tanaka (1988) lias derived the influence functions, which are equivalent to the perturbation expansions up to linear terms, of two functions of eigenvalues and eigenvectors of a real symmetric matrix, and applied them to principal component analysis. The present paper deals with the perturbation expansions up to quadratic terms of the same functions and discusses their application to sensitivity analysis in multivariate methods, in particular, principal component analysis and principal factor analysis. Numerical examples are given to show how the approximation improves with the quadratic terms.