Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données

Every bivariate distribution function with continuous marginals can be represented in terms of a unique copula, that is, in terms of a distribution function on the unit square with uniform marginals. This paper is concerned with a special class of copulas called Archimedean, which includes the uniform representation of many standard bivariate distributions. Conditions are given under which these copulas are stochastically ordered and pointwise limits of sequences of Archimedean copulas are examined. We also provide two new one-parameter families of bivariate distributions which include as limiting cases the Frechet bounds and the independence distribution.     

The strong uniform convergence of multivariate variable kernel estimates

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and f_n is the variable kernel estimate Here H_ni is the distance between X_i and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn     

An operative extension of the likelihood ratio test from fuzzy data

In the present paper we are going to extend the likelihood ratio test to the case in which the available experimental information involves fuzzy imprecision (more precisely, the observable events associated with the random experiment concerning the test may be characterized as fuzzy subsets of the sample space, as intended by Zadeh, 1965). In addition, we will approximate the immediate intractable extension, which is based on Zadeh’s probabilistic definition, by using the minimum inaccuracy principle of estimation from fuzzy data, that has been introduced in previous papers as an operative extension of the maximum likelihood method.     

一人多机的动态配置模型及其解法

本文以机械企业为背景,探讨了一人多机看管问题中的人员配置问题,并采用层次序列法对人员配置数学模型进行了求解,给出了启发式解法,指出了进一步研究的方向。     

偏振光的双光束与多光束干涉

本文通过时平面偏振光的双光束与多先束干涉现象的讨论，使对偏振光的干涉有进一步的认识，并计算出偏振光照明条件下，光栅的光强分布和分辨本领。     

吴越文化的分野

吴与越互为近邻，语言相通，舟楫相同；但二次南下的夏文化与会稽地区鸟图腾族文化相结合，形成越文化；东下的周文化与太湖平原的鱼族文化相结合，形成吴文化。他们由于种族血统、宗教信仰、生活习俗的差异，以及对待中原文化的态度不同，吸收华夏文化的程度不同。使吴文化和越文化各具有自己的个性和特色。     

拒不说明巨额财产来源罪探讨

本文从维护廉政制度角度,提出“拒不说明巨额财产来源”侵害的是国家机关的正常活动和廉政制度双重客体;表现为行为人拒不履行保持公正廉洁的特定义务;其犯罪主体是国家工作人员:其主观方面是由故意构成。据上设“拒不说明巨额财产来源罪”成立。     

The behavior of the battered child: A behavioral deficiency syndrome resulting from developmental interferences and reactive learning

Behavioral observation of battered children reveals a generalized syndrome consisting of apathy, social isolation, emotional constriction, aggression, and intellectual, motor and language retardation. This syndrome is considered to be a ‘behavioral deficiency syndrome.’ Developmental interference imposed by abusive parents upon the child, and subsequent reactive learning by the child are discussed as etiological factors in the development of this syndrome. Implication of these etiological factors for therapy of the abusive family are also discussed.