Estimation of p{x > y} based on progressively truncated versions of the wilcqxon-mann-whitney statistics

Stochastic processes related to some generalized U-statistics (with especial emphasis on the Wilcoxon-Mann-Whitney (WMW-) statistic), under progressive right censoring, are considered for prediction purposes. Their weak convergence results are incorporated in the study of the asymptotic properties of the predictors. The form of the estimable parameter as a function of the truncation point is studied for the WMW case for some typical distributions and the theoretical results are supplemented by simulated ones.     

The discretely observed immigration-death process: Likelihood inference and spatiotemporal applications

ABSTRACT

We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.     

On generalized exponential transformations for proportions

ABSTRACT

Transformation of the response is a popular method to meet the usual assumptions of statistical methods based on linear models such as ANOVA and t-test. In this paper, we introduce new families of transformations for proportions or percentage data. Most of the transformations for proportions require 0 < x < 1 (where x denotes the proportion), which is often not the case in real data. The proposed families of transformations allow x = 0 and x = 1. We study the properties of the proposed transformations, as well as the performance in achieving normality and homoscedasticity. We analyze three real data sets to empirically show how the new transformation performs in meeting the usual assumptions. A simulation study is also performed to study the behavior of new families of transformations.     

Humerical. Results concerning the mle of an exponential parameter used in life testing

It was previously shown that the maximum likelihood estimator 0 of the scale parameter of the exponential distribution is asymptotically normal for type-I censoring. Applicability of the asymptotic normality results for finite samples is studied here by computer simulation for several different normalizing factors and for various levels of censoring. The use of the asymptotic results in statistical problems is illustrated by an example     

Minimum anderson-darling estimation

The Anderson-Darling distance d(F_n ,F_0,) between the empirical distribution function F_n and the hypothesized model F₀ is minimized to produce estimators with good robustness and efficiency properties. In addition, the residual distance d_min = min₀d(F_n,F₀.) is availabe to assess model validity. The approximate distribution-free character of nd_min is studied using monte carlo methods.     

Asymptotic Comparison of Two Discriminants Used in Normal Covariate Classification

In this paper, we examine the performance of Anderson's classification statistic with covariate adjustment in comparison with the usual Anderson's classification statistic without covariate adjustment in a two-population normal covariate classification problem. The same problem has been investigated using different methods of comparison by some authors. See the bibliography. The aim of this paper is to give a direct comparison based upon the asymptotic probabilities of misclassification. It is shown that for large equal sample size of a training sample from each population, Anderson's classification statistic with covariate adjustment and cut-off point equal to zero, has better performance.     

A re-appraisal of tests for normality

Tests for normality can be divided into two groups - those based upon a function of the empirical distribution function and those based upon a function of the original observations. The latter group of statistics test spherical symmetry and not necessarily normality. If the distribution is completely specified then the first group can be used to test for ‘spherical’ normality. However, if the distribution is incompletely specified and F‘‘x_i - x’/s’ is used these test statistics also test sphericity rather than normality. A Monte Carlo study was conducted for the completely specified case, to investigate the sensitivity of the distance tests to departures from normality when the alternative distributions are non-normal spherically symmetric laws. A “new” test statistic is proposed for testing a completely specified normal distribution     

Two tests for monotone failure rate with incomplete data

Two statistics are proposed for testing for the exponential distribution against monotone failure rate alternatives when ran-domly right censored data are available. One of them is a general-ization of the Billmann, Antle and Bain test based on the MLE of the shape parameter of the Weibull distribution. The second has the advantage of being given in closed form. For this test the asymptotic null distribution is given. Consistency of the two tests is proved starting from an expected value inequality characterizing monotone failure rate.     

Efficiencies of some two–sample location tests for a broad class of distributions

Efficiencies of variety of two–sample tests are examomed for a broad class of distributions. Two new test statistics are introduced. and their potential use as part of an adaptive procedure discussed. Recommendations are made as to the utility of the various test statistics when the underlying distribution is unknown.