Some Characterizations Based on Entropy of Order Statistics and Record Values

In the literature of information theory, Shannon entropy plays an important role and in the context of reliability theory, order statistics and record values are used for statistical modeling. The aim of this article is characterizing the parent distributions based on Shannon entropy of order statistics and record values. It is shown that the equality of the Shannon information in order statistics or record values can determine uniquely the parent distribution. The exponential distribution is characterized through maximizing Shannon entropy of record values under some constraints. The results are useful in the modeling problems.     

Computing A-optimal Designs for Weighted Polynomial Regression by Taylor Expansion

This article is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m ? a, m + a], m, a > 0. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points, and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursive procedure for calculating the A-optimal designs. Examples are presented to illustrate the procedures for computing the optimal designs.     

Local Weighted Average Estimation of the Regression Operator for Functional Data

We are concerned with the problem of local weighted average estimation of the regression operator when the responses are real-valued random variables, the explanatory data are of functional fixed-design type, and the errors consist of an independent and identically distributed variables. In this article, our main contributions on the local linear functional estimation concern from one part, the situation when the data are of functional fixed-design kind, and from the other part, in deriving uniform asymptotic results on the behavior of this estimator with respect to the topological properties of the space data (normed or semi-metric).     

The Empirical Likelihood Inference of a Regression Parameter in Censored Partial Linear Models Based on a Piecewise Polynomial

This article aims at making an empirical likelihood inference of regression parameter in partial linear model when the response variable is right censored randomly. The present studies are mainly designed to use empirical likelihood (EL) method based on synthetic dependent data, and the result cannot be applied directly due to the unknown weights in it. In this paper, we introduce a censored empirical log-likelihood ratio and demonstrate that its limiting distribution is a standard chi-square distribution. The estimating procedure of β is developed based on piecewise polynomial method. As a result, the p-value of test and the confidence interval can be obtained without estimating other quantities. Some simulation studies are conducted to highlight the performance of the proposed EL method, and the results show a good performance. Finally, we apply our method into the real example of multiple myeloma data and show the proof of theorem.     

Empirical likelihood-based serial correlation testing in partially varying coefficient single-index models

ABSTRACT

Partially varying coefficient single-index models (PVCSIM) are a class of semiparametric regression models. One important assumption is that the model error is independently and identically distributed, which may contradict with the reality in many applications. For example, in the economical and financial applications, the observations may be serially correlated over time. Based on the empirical likelihood technique, we propose a procedure for testing the serial correlation of random error in PVCSIM. Under some regular conditions, we show that the proposed empirical likelihood ratio statistic asymptotically follows a standard χ² distribution. We also present some numerical studies to illustrate the performance of our proposed testing procedure.     

Matrix variate Macdonald distribution

Abstract

In this article, we generalize the univariate Macdonald distribution to the matrix case and give its derivation using matrix variate gamma distribution. We study several properties such as cumulative distribution function, marginal distribution of submatrix, triangular factorization, moment generating function, and expected values of several functions of the Macdonald matrix. Some of these results are expressed in terms of special functions of matrix arguments and zonal polynomials.     

中国网络政治参与主体的特征--基于多项式回归模型的实证分析

基于大样本的网络问卷调查构建了多项式回归模型,从人口统计特征、网络基本使用特征、网络政治参与行为特征和对网络政治参与效果的态度四个方面,对中国网络政治参与主体的结构与特征进行了探讨。这些特征主要是:参与主体为年纪轻、高学历、高收入、高素质、赋有理性的群体;现实社会中职业声望与网络话语权并不完全匹配,甚至是对立的;社会化媒体成为网络政治参与的主要工具,特别是微博在网络维权上发挥着独特的作用;公民网络政治参与的主要目的是自我实现。     

带变量核的分数次极大算子在加权Morrey 空间上的有界性

利用核函数Ω的性质,证明了带变量核的分数次极大算子MΩ,α是加权Morrey空间Lp,k（ω）上的有界算子,从而推广了以往非变量核的结果．     

基于单向函数与二元多项式的秘密分享方案

基于二元多项式的秘密分享方案,利用单向函数和二元多项式构造了一个(t+1,n)门限秘密分享方案.该方案易实现成员的加入和系统的更新.     

不定度规空间上的一类带有移条件的Sturm-Liouville问题的自共轭性

本文围绕不连续奇异微分算子的自共轭性进行研究,微分算子的自共轭性是线性算子理论中十分重要的问题.文章主要研究了定义在一个新的完备的不定度规空间下的带有转移条件的Sturm-Liouville问题,最终证明了算子在不定度规空间下的自共轭性。