Rate of convergence for the distribution of the spearman-karber estimator

A Berry-Esseen type of bound is obtained for the error of the normal approximation to the distribution of the Spearman-Karber estimator. It is shown that this bound is of the order of the square root of the common dose mesh.     

The power of two exact tests for structural change in the presence of heteroskedasticity

This paper compares analytically the power of the Jayatissa (1977) and Tsurumi (1984) tests for structural change in a heteroskedastic normal linear regression model with two equal-sized independent sub-samples. It is shown that the non-centrality parameter of the Tsurumi test cannot exceed that of the Jayatissa test and some conditions are obtained under which one test dominates the other.     

On unbiased estimation of gini index and yntema-pietra index of lognormal distribution and their variances

Here we derive the uniformly minimum variance unbiased (best) estimator and a strongly consistent, asymptotically normal, unbiased estimator of each of Gini index and Yntema-Pietra index of lognormal distribution . These estimators are in terms of generalized hypergeometric functions ₁F₂. Further, the variances of these estimators and the best estimators of variances of best estimators are found out. They are in terms of Kempé de Fériet's hypergeometric functions.     

Asymptotic normality of MRPP statistics from invariance principles of u-statistics

Multi-response permutation procedures (MRPP) were recently introduced to test differences between a priori classified groups of objects ( Mielke, Berry Johnson, 1976; Mielke, 1979 ). The null distributions of the MRPP statistics were initially conjectured to be asymptotically normal for some specified conditions within the setting of a sequence of finite populations due to Madow ( 1948 ).

Asymptotic normality of a class of MRPP statistics (under the null hypothesis) is shown in two cases: (i) the setting which considers the populations to be the samples resulting from sequential independent identically distributed (i.i.d.) sampling (sampling from infinite populations) and (ii) the setting of a sequence of increasingly large finite populations (sampling from finite populations). The results are direct applications of the weak convergence of a U-statistic process in the i.i.d. case to a Brownian motion (Bhattacharyya and Sen, 1977) and of the weak convergence of a U-statistic process in the finite populations case to a Brownian bridge (Sen, 1972). The conditions are milder for the i.i.d. case than for the finite populations case. However, neither case provides a restriction of a practical consequence in applications of MRPP. In either case, convergence is shown to depend on the asymptotic ratios of the group sizes to the population size.     

Dependence structures and asymptotic properties of Baker's distributions with fixed marginals

We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions. The properties include the weak convergence to the Fréchet–Hoeffding upper bound, the product-moment convergence, as well as the dependence structures TP₂ (totally positive of order 2), or MTP₂ (multivariate TP₂). In proving the weak convergence, a generalized local limit theorem for binomial distribution is provided.     

论英语否定结构中的歧义现象

在含有否定结构的英语句中 ,如果是一个孤立的句子 ,往往会令读者觉得含有多种理解或者有多种意义。这就是在英语否定结构中常出现的歧义现象 ,这种否定结构即是英语歧异结构之一。了解这种结构和现象 ,就能知道这种结构的正确意义 ,从而避免歧义 ,避免理解或表达的错误     

对《新著国语文法》析句法的再认识

<新著国语文法>是我国首部系统地描写白话文的语法著作.作为一部传统语法学的代表著作,它与后来影响中国的结构主义语言学的语法理论和分析方法存在较大分歧.但是在语言教学与研究的实践中,这种分歧并不是非此即彼的.面对包罗万象的语言世界,单一、静态的语法体系很难给予充分的描写和解释,而研究目的和侧重点的不同也会对不同语法体系的形成起到重要作用.     

On von Mises type conditions for p-max stable laws, rates of convergence and generalized log Pareto distributions

In this article we obtain an alternative formulation of the von Mises type conditions for p-max stable laws in terms of generalized log Pareto distributions (glogPds). Relationship between the rate of convergence of extremes and the remainder terms in the von Mises type conditions is investigated. It is shown that the rate of convergence in the von Mises type conditions for p-max stable laws determines the distance of the underlying distribution function from a glogPd.