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.     

Local efficiency of moment estimators in beta-binomial model

In this paper, the beta-binomial model is introduced as a Markov chain. It is shown that the correlated binomial model of Kupper and Haseman (1978) is identical to the additive binomial model of AItham(1978) and both are a first order approximation of the beta-binomial model. For small γ, the local efficiency of the moment estimators for the mean ρ and the extra-binomial variation γ is examined analytically. It is shown that, locally, the moment estimator for p is efficient up to the second order of y. Exact formulae for the relative efficiency are obtained for both the cases with γ known and unknown. Generalization to the unequal sample size case is also carried out. In particular, the gain in efficiency by using the quasi-likelihood estimator instead of the ratio estimator for p is studied when γ is known. These results are in agreement with the Monte Carlo results of Kleinman(1973) and Crowder(1985).     

Nonparametric prediction analysis for binary data

A nonparametric inference algorithm developed by Davis and Geman (1983) is extended problem. The algorithm and applied to a medical prediction employs an estimation procedure for acquiring pairwise statistics among variables of a binary data set, allows for the data-driven creation of interaction terms among the variables, and employs a decision rule which asymptotically gives the minimum expected error. The inference procedure was designed for large data sets but has been extended via the method of cross-validation to encompass smaller data sets.     

Continuous outcomes stochastically mismeasured as discrete random variables: a maximum likelihood approach

In an economic model of retirement behavior, a continuous dependent variable was required; the variable could only be estimated discretely with error, however. Parameter estimates using this dependent variable and ordinary least squares regression are inefficient. In th is paper, we develop a maximum likelihood procedure which adjusts for this heteroscedasticity.     

Some Properties of Weighted Distributions in the Context of Repairable Systems

ABSTRACT

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables.     

Goodness-of-Fit Tests for Multivariate Distributions

We propose three new statistics, Z _p , C _p , and R _p for testing a p-variate (p ≥ 2) normal distribution and compare them with the prominent test statistics. We show that C _p is overall most powerful and is effective against skew, long-tailed as well as short-tailed symmetric alternatives. We show that Z _p and R _p are most powerful against skew and long-tailed alternatives, respectively. The Z _p and R _p statistics can also be used for testing an assumed p-variate nonnormal distribution.     

On Upshifted Reversed Mean Residual Life Order

Recently, the concept of reversed mean residual life order based on the mean of the random variable X _t  = (t ? X | X ≤ t), t > 0, called the reversed residual life, defined for the nonnegative random variable X, has been introduced in the literature. In this paper, a stochastic order based on the shifted version of the reversed mean residual life is proposed, based on the reversed mean residual life function for a random variable X with support (l _X , ∞), where l _X may be negative infinity, and its properties are studied. Closure under the Poisson shock model and properties for spare allocation are also discussed.     

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.