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.     

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.     

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.     

Setting the clock back to zero property of a class of bivariate life distributions

In a previous paper. B. R. Rao and Talwalker (1993) considered absolutely continuous life distributions and extended the Lack of Memory Property (L.M.P.) of the exponential distribution and showed that several classes of life distributions have this property, which was called the 'setting the clock back to zero' property. ¶Its analog is discussed in the present paper for hivariate and multivariate classes of life distributions. As a simple application of this analog, it is proved that the Life expectancy and the Percentile Residual Life vectors of a population of individuals under the influence of multiple competing risks have simple expressions if the class of their joint life distributions has the setting the clock back to zero property,     

Best linear predictors for factor scores

From the literature three types of predictors for factor scores are available. These are characterized by the constraints: linear, linear conditionally unbiased, and linear correlation preserving. Each of these constraints generates a class of predictors. Best predictors are defined in terms of Lowner's partial matrix order applied to matrices of mean square error of prediction. It is shown that within the first two classes a best predictor exists and that it does not exist in the third.     

Estimation of the number of jumps of the jump regression functions

This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the difference between right and left onesided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided.     

A Similarity Measure Based on Species Proportions

ABSTRACT

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996 Smith , W. , Solow , A. R. , Preston , P. E. ( 1996 ). An estimator of species overlap using a modified beta-binomial model. Biometrics 52 : 1472 – 1477 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.     

Diagnosis of Multivariate Control Chart Signal Based on Dummy Variable Regression Technique

Abstract

It is common to monitor several correlated quality characteristics using the Hotelling's T ² statistic. However, T ² confounds the location shift with scale shift and consequently it is often difficult to determine the factors responsible for out of control signal in terms of the process mean vector and/or process covariance matrix. In this paper, we propose a diagnostic procedure called ‘D-technique’ to detect the nature of shift. For this purpose, two sets of regression equations, each consisting of regression of a variable on the remaining variables, are used to characterize the ‘structure’ of the ‘in control’ process and that of ‘current’ process. To determine the sources responsible for an out of control state, it is shown that it is enough to compare these two structures using the dummy variable multiple regression equation. The proposed method is operationally simpler and computationally advantageous over existing diagnostic tools. The technique is illustrated with various examples.