Characterizations of geometric distribution through progressively Type-II right-censored order statistics

In this paper, we consider characterizations of geometric distribution based on some properties of progressively Type-II right-censored order statistics. Specifically, we establish characterizations through conditional expectation, identical distribution, and independence of functions of progressively Type-II right-censored order statistics. Moreover, extensions of these results to generalized order statistics are also sketched. These generalize the corresponding results known for the case of ordinary order statistics.     

Theory and methods for partitioned Gini coefficients computed on post-stratified data

The Gini coefficient is used to measure inequality in populations. However, shifts in the population distribution may affect subgroups differently. Consequently, it can be informative to examine inequality separately for these segments. Consider an independently and identically distributed sample split based on ranking and compute the Gini coefficient for each partition. These coefficients, calculated from post-stratified data, are not functions of U-statistics. Therefore, previous theoretical and methodological results cannot be applied. In this article, the asymptotic joint distribution is derived for the partitioned coefficients and bootstrap methods for inference are developed. Finally, an application to per capita income across census tracts is examined.     

False discovery rate control for non-positively regression dependent test statistics

In this paper we present a modification of the Benjamini and Hochberg false discovery rate controlling procedure for testing non-positive dependent test statistics. The new testing procedure makes use of the same series of linearly increasing critical values. Yet, in the new procedure the set of p-values is divided into subsets of positively dependent p-values, and each subset of p-values is separately sorted and compared to the series of critical values. In the first part of the paper we introduce the new testing methodology, discuss the technical issues needed to apply the new approach, and apply it to data from a genetic experiment.     

Censored Kullback-Leibler Information and Goodness-of-Fit Test with Type II Censored Data

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Then we establish a goodness-of-fit test statistic based on the censored Kullback-Leibler information with the type 2 censored data, and compare the test statistics with some existing test statistics for the exponential and normal distributions.     

Bayesian inference for circular distributions with unknown normalising constants

Very often, the likelihoods for circular data sets are of quite complicated forms, and the functional forms of the normalising constants, which depend upon the unknown parameters, are unknown. This latter problem generally precludes rigorous, exact inference (both classical and Bayesian) for circular data.Noting the paucity of literature on Bayesian circular data analysis, and also because realistic data analysis is naturally permitted by the Bayesian paradigm, we address the above problem taking a Bayesian perspective. In particular, we propose a methodology that combines importance sampling and Markov chain Monte Carlo (MCMC) in a very effective manner to sample from the posterior distribution of the parameters, given the circular data. With simulation study and real data analysis, we demonstrate the considerable reliability and flexibility of our proposed methodology in analysing circular data.     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.     

Csiszar’s ϕ-divergences for testing the order in a Markov chain

x ₁, ..., x _n+r can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis H ₀ that a chain of order r− 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: _ϕ-Divergences. More precisely, if p _{a 1 ....., a r}: _{a r +1} denotes the transition probability for a r ^th order Markov chain, the hypothesis to be tested is H ₀:p _{a 1 ....., a r}: _{a r +1} = p _{a 2 ....., a r}: _{a r +1}, a _i ∈{1, ..., s}, i = 1, ..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic. Received: August 3, 1998; revised version: November 25, 1999     

传统统计面对的挑战

针对统计的黑匣子特性,借用Breiman的两种统计文化的平台,分析传统统计面临的挑战和危机,并探索统计领域究竟要向何处发展的问题。研究表明：统计学必须重新回到针对实际问题而与数据打交道,并且创造有关理论的传统上来。只有这样,才能应对不断产生的新问题所带来的挑战。     

Tests for symmetry about an unknown value based on the empirical distribution function

A class of Kolmogorov-Smirnov and Cramér-von Mises type statistics for testing symmetry about an unknown value is described. These statistics are not distribution-free, however, and, indeed, are not readily amenable to calculation. A linear rank statistic analog of the first component of the Cramér-von Mises type statistic is investigated. Asymptotic non-null properties of these procedures in the normal case are studied, and an efficiency comparison of the Cramér-vonMises statistic, the linear rank statistic analog, the modified Wil-coxon statistic, and the likelihood ratio test is reported.     

甘蓝型油菜品种区试资料的非参数度量

应用秩次变量nij 和nij',非参数统计量Pi、Pi'、Si 和Dj 描述 1999年长江上游油菜品种区域试验资料。结果表明 :94 0 7N丰产性、稳产性最好 ,94杂 - 3、黔杂 97- 2次之。油 2 71丰产性最差 ,绵阳92 - 4 592稳产性最差。除曲靖、昆明点之外 ,其余试验点具有较好的代表性