Large deviation local limit theorems for ratio statistics

Let {T_n, n ≥ 1} be an arbitrary sequence of nonlattice random variables and let {S_n, n ≥ 1} be another sequence of positive random variables. Assume that the sequences are independent. In this paper we obtain asymptotic expression for the density function of the ratio statistic R_n = T_n/S_n based on simple conditions on the moment generating functions of T_n and S_n. When S_n = re, our main result reduces to that of Chaganty and Sethura-man[Ann. Probab. 13(1985):97-114]. We also obtain analogous results when T_n and S_n are both lattice random variables. We call our theorems large deviation local limit theorems for R_n, since the conditions of our theorems imply that R_n → c in probability for some constant c. We present some examples to illustrate our theorems.     

Estimation of the population spectral distribution from a large dimensional sample covariance matrix

This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Mar?enko–Pastur equation, originally defined in the complex plane, to the real line. Beyond its easy implementation and the established asymptotic consistency, the new estimator outperforms two existing estimators from the literature in almost all the situations tested in a simulation experiment. An application to the analysis of the correlation matrix of S&P 500 daily stock returns is also given.     

多个大股东存在下的董事会结构模型及其实证检验

考虑到我国普遍存在大股东集中持股的客观现实,基于大股东"掏空"动机,区分大股东间"监督"与"合谋"两种不同关系,本文构建多个大股东存在下的董事会结构理论模型,并结合该模型的理论涵义推演出研究假设.以1999-2005年A股上市公司为样本对理论模型进行实证检验,结果表明,董事会中内部董事比例和第一大股东选派的外部董事比例都随第一大股东持股比例的增加而增加,随第二大股东持股比例的增加而减少;此外,当公司的终极控制为国有性质的时候,内部董事和第一大股东选派的外部董事比例更大,而独立董事比例则更少.实证检验的结果验证了理论模型的理论预期.表明所提出的理论模型能够揭示多个大股东存在下董事会的结构特征.同时印证了模型构建的正确性.     

论大小金川战争中碉楼的作用

碉楼是羌、藏等少数民族在古代修建的一种独具特色的建筑,平时居住及储藏物资,战时则用以防范外来势力的进攻。清朝乾隆年间,中央王朝对大小金川的用兵,大小金川土司除了依仗天时、地势和人力外,更重要的是倚恃碉楼的防御体系抵抗清朝官兵,致使大小金川战争成为乾隆帝“十全武功”中历时最长、耗资颇巨、伤亡甚重的一次战争。     

A classifier under the strongly spiked eigenvalue model in high-dimension,low-sample-size context

Abstract

We consider the classification of high-dimensional data under the strongly spiked eigenvalue (SSE) model. We create a new classification procedure on the basis of the high-dimensional eigenstructure in high-dimension, low-sample-size context. We propose a distance-based classification procedure by using a data transformation. We also prove that our proposed classification procedure has consistency property for misclassification rates. We discuss performances of our classification procedure in simulations and real data analyses using microarray data sets.     

Large Deviations for Sums of Independent Non Identically Distributed Random Variables

This article considers large deviation results for sums of independent non identically distributed random variables, generalizing the result of Petrov (1968 Petrov , V. V. ( 1968 ). Asymptotic behavior of probabilities of large deviations . Theor. Probab. Appl. 13 : 408 – 420 . [Google Scholar]) by using a weaker and more natural condition on bounds of the cumulant generating functions of the sequence of random variables.     

Inference for Mixtures

In this article, we consider the problem of estimating certain “parameters” in a mixture of probability measures. We show that a single sample is typically suitable for estimating the component measures, but not suitable for estimating the mixing measures, especially when consistency is required. To have consistent estimators of the mixing measure, several samples with increasing size are needed in general.     

Some Limit Results for Pareto Random Variables

We sample m (m ≥ 1) i.i.d. Pareto random variables with the density function x ^?2 (x ≥ 1) and establish two large deviations for the partial sums. In addition, the maxima of sums of the two-tailed Pareto random variables is discussed and some asymptotical forms are obtained also.