A note on a parametric extension of rank tests to the analysis of multifactor experiments within blocks

A general rank test procedure based on an underlying multinomial distribution is suggested for randomized block experiments with multifactor treatment combinations within each block. The Wald statistic for the multinomial is used to test hypotheses about the within–block rankings. This statistic is shown to be related to the one–sample Hotellingt's T² statistic, suggesting a method for computing the test statistic using the standard statistical computer packages.     

A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2 M Full Factorial Designs

ABSTRACT

In this article we present a new solution to test for effects in unreplicated two-level factorial designs. The proposed test statistic, in case the error components are normally distributed, follows an F random variable, though our attention is on its nonparametric permutation version. The proposed procedure does not require any transformation of data such as residualization and it is exact for each effect and distribution-free. Our main aim is to discuss a permutation solution conditional to the original vector of responses. We give two versions of the same nonparametric testing procedure in order to control both the individual error rate and the experiment-wise error rate. A power comparison with Loughin and Noble's test is provided in the case of a unreplicated 2⁴ full factorial design.     

Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.     

A Note on Influence Assessment in Score Tests

Recently, [1] Ebrahimi, N. 1996. How to measure uncertainty about residual life time. Sankhya Ser. A, 58: 48–57.  [Google Scholar] proposed a dynamic measure based on differential entropy applied to the residual lifetime. This measure has been used for the classification and ordering of survival functions. More recently, [2] Ebrahimi, N. 1997. Testing whether lifetime distribution is decreasing uncertainty. Journal of Statistical Planning and Inference, 64: 9–19. [Crossref], [Web of Science ®] , [Google Scholar] has considered the problem of testing the monotonicity of this measure. We propose and study several kernel type estimators of the entropy of residual life through the estimation of f(x) log f(x). These estimators can be applied to the classification and comparison of lifetime distribution.     

Combining Univariate Tests for Multivariate Location Problem

In this article, three methods of combining dependent univariate tests are studied. The Bahadur approximate efficiencies are derived under the asymptotic normal assumption. These procedures are applied to the multivariate location problem and compared with two Hotelling-type tests. A Monte Carlo study indicates that in certain cases the powers of the combination methods are much better than Hotelling's T ² and other multivariate nonparametric tests.     

Dynamic Copula-Based Markov Time Series

This article examines a test procedure for checking the constancy of serial dependence via copulas for Markov time series data. It also provides a copula-based modeling approach for the dynamic serial dependence. Various parametric families of copulas offering different dependent structures are investigated. A score test is proposed for checking the constancy of a copula parameter. The score test is constructed and its asymptotic null distribution established under a two-stage estimation procedure. The test does not require specification of the probability distribution for the copula parameter. To capture the dynamics of dependence structure over time, autoregressive moving average and exponential type models are proposed. Illustrations are given based on simulated data and historic coffee prices data.     

Gluing Copulas

We present a new way of constructing n-copulas, by scaling and gluing finitely many n-copulas. Gluing for bivariate copulas produces a copula that coincides with the independence copula on some grid of horizontal and vertical sections. Examples illustrate how gluing can be applied to build complicated copulas from simple ones. Finally, we investigate the analytical as well as statistical properties of the copulas obtained by gluing, in particular, the behavior of Spearman's ρ and Kendall's τ.     

On some tests for independence in nonnormal situations: neyman'S C(A)test

A study is made of Neyman's C(a) test for testing independence in nonnormal situations. It is shown that it performs very well both in terms of the level of significance and the powereven for smallvalues of the samplesize. Also, in the case of the bivariate Polsson distribution, itis shown that Fisher's z and Student's t transforms of the sample correlation coefficient are good competitors for Neyman's procedure.

     

Moments for a ratio of correlated gamma variates

This paper considers the finite integral moments for the ratio, R = X/Y, where X and Y re correlated gamma distributed variables. An analytical and numerical comparison is given for two classes of underlying bivariate gamma distributions. It is shown that the two bivariate gamma structures provide indentical experessions for the mth unadjussted moment, E(R^m), if and only if either of the following conditions hold : 1) X and Y are uncorrelated of 2) m=1. A numerical evaluation is performed to determine the extent that the two methods differ whenever the variables are correlated