High dimensional asymptotics for the naive Hotelling T2 statistic in pattern recognition

Abstract

This paper examines the high dimensional asymptotics of the naive Hotelling T² statistic. Naive Bayes has been utilized in high dimensional pattern recognition as a method to avoid singularities in the estimated covariance matrix. The naive Hotelling T² statistic, which is equivalent to the estimator of the naive canonical correlation, is a statistically important quantity in naive Bayes and its high dimensional behavior has been studied under several conditions. In this paper, asymptotic normality of the naive Hotelling T² statistic under a high dimension low sample size setting is developed using the central limit theorem of a martingale difference sequence.     

Comparing a New Gini Test with Other Symmetry Tests When Median Is Unknown

Although there exists an ample literature on the tests of univariate symmetry, each article provides comparison of few selected competitors only. We are comparing the performance of 15 tests recommended in the literature and two new methods introduced by Auda (2006 Auda (Ouda), H. 2006. New Tests of Univariate Symmetry Based on the Gini Mean Difference, Kalamazoo, MI: Western Michigan University. Ph.D. thesis [Google Scholar]). One of them, rank-based test RS, compares favorably with several existing procedures in controlling the Type I error as well as in power as shown in our comprehensive simulation study. An important novelty in the article are Figs. 1– 3 enabling comparison of Type I error probabilities and power of the 16 tests for 17 null and 19 alternative distributions.     

Ranking paired contestants

The ranking of paired contestants (players) after a series of contests is difficult when every player does not play every other player. In the 1975 JASA Mark Thompson presented a maximum likelihood solution based on the assumption that the probability of any one player defeating any other is a function only of the difference in their ranks. Here the linear approximation to that likelihood is shown to lead to a nonparametric measure of the efficacy of the ranking, called the net difference in ranks (NDR) , which is the sum of the differences in ranks of the paired players in the observed contests that agree with the ranking minus the sum of the differences in ranks in the observed contests that disagree with the ranking (upsets) . The subject is part of a large literature that has been consolidated by H.A. David in The Method of Paired Comparisons (1963, 1988). The method was introduced by the psychophysicist Fechner in 1860 and has been widely applied to sensory testing,     

Least significant spacing for ‘one versus the rest’ normal populations

Consider sample means from k(≥2) normal populations where the variances and sample sizes are equal. The problem is to find the ‘least significant difference’ or ‘spacing’ (LSS) between the two largest means, so that if an observed spacing is larger we have confidence 1 - α that the population with largest sample mean also has the largest population mean.

When the variance is known it is shown that the maximum LSS occurs when k = 2, provided a < .2723. In other words, for any value of k we may use the usual (one-tailed) least significant difference to demonstrate that one population has a population mean greater than (or equal to) the rest.

When the variance is estimated bounds are obtained for the confidence which indicate that this last result is approximately correct.     

‘Trapped between two worlds’ – Muslim Palestinian women from Israel in Jordanian universities: new identity and the price it demands

Interviews were held with 12 Muslim Palestinian women from Israel, presently studying in Jordan (6) or who had completed their higher education in Jordan (6). They explained the factors that pushed or pulled them to study in Jordan, the independence that they experienced there, the empowerment they achieved, and the price they paid when they returned to Arab society in Israel. The Arab cultural space in Jordan is defined as both foreign and close, due to its geographical and cultural proximity, and yet its distance from home and patriarchal supervision. The research findings indicate that this situation influences the formation of these women's gender identity and their empowerment but also creates much pain and conflict. The Palestinian women's new identity, formed during their studies, assists them in their efforts to reintegrate and establish their status when they return from their academic studies abroad to their society of origin, Muslim Arab society in Israel.     

Identity,difference and community in Southern Irish Protestantism: The Protestants of West Cork

This article looks at how the Protestants of West Cork came to terms with Irish independence, and how they have responded to the major social and political changes of the past decades. West Cork Protestants are geographically peripheral to the Southern Protestant population as a whole, and have a weaker socio-economic profile. They live in an area that saw some of the fiercest fighting and worst atrocities in the war of independence and civil war. Their experience throws considerable light on issues of whether Protestants were a privileged or oppressed minority, and whether and how they integrated into the new state. Extensive in-depth interviews are used to show how West Cork Protestants reconstructed their identity, defined their differences from Catholics and maintained community in the years since independence.     

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.     

Some characterizations of discrete distributions based on weak records

Let X ₁, X ₂,... be iid random variables (rv's) with the support on nonnegative integers and let (W _n , n≥0) denote the corresponding sequence of weak record values. We obtain new characterization of geometric and some other discrete distributions based on different forms of partial independence of rv's W _n and W _n+r —W _n for some fixed n≥0 and r≥1. We also prove that rv's W ₀ and W _n+1 —W _n have identical distribution if and only if (iff) the underlying distribution is geometric.     

跨文化沟通与国际经济

搞好跨文化沟通是国际经济活动成功的重要条件.本文以西欧、美国、阿拉伯国家和日本为对象探讨其文化差异和沟通的途径.     

试析革命家毛泽东与文学家鲁迅文艺观的差异

毛泽东与鲁迅尽管在文艺思想上有着许多相同或相似的观点,但细究起来,他们之间的确存在着明显的差异:毛泽东主要是从民族斗争和阶级斗争的角度来认识文艺的性质和作用的,其中心思想是阶级论、人民性和工具论,相对而言却较为忽视文艺的独立性、审美价值和艺术规律;而鲁迅则是以文艺为本位,较多强调文艺独立于政治的特殊性以及尊重并服从文艺规律,侧重点在于文艺的思想性、规律性和审美价值。产生这些差异的主要原因是他们各自所处的历史地位以及对中国社会、历史、文学考察和认识角度的不同。