Density estimation for samples satisfying a certain absolute regularity condition

Let {ξ_i} be an absolutely regular sequence of identically distributed random variables having common density function f(x). Let H_k(x,y) (k=1, 2,…) be a sequence of Borel-measurable functions and f_n(x)=n^?1(H_n(x,ξ₁)+…+H_n(x,ξ_n)) the empirical density function. In this paper, the asymptotic property of the probability P(sup_x|f_n(x)?f(x)|>ε) (n→∞) is studied.     

THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

A GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1

A Galton-Watson process in varying environments (Z_n), with essentially constant offspring means, i.e. E(Z_n)/mⁿ→α∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Z_n)_n grows like 2ⁿon A and like mⁿon B (m > 4).     

以网络为平台的大学生组织生活质量模式探析

目前,大学生组织生活存在内容不够丰富、形式缺乏吸引力,成员沟通交流不足、缺乏民主互动氛围,组织生活缺少针对性和系统性等问题。借助网络平台可以便捷地运用党员教育资源,有效扩大党员教育的辐射度与受益面,从而增强组织生活的吸引力。因此,通过构建党建网络体系和党建教育信息库、网络党支部平台、网上党校平台、网上组织生活的在线交流平台等途径,可以行之有效地对大学生党员进行引导和教育。     

论西方国家的司法审查制度

西方国家的司法审查是指通过司法程序审查立法和行政是否违宪的一种制度,普遍认为这一制度首先起源于美国。司法审查机构一般可分为普通法院和宪法法院两种,通过具体审查、抽象审查、宪法诉讼等方式进行。在不同的审查模式下,用判例、惯例或制定专门法律来保障这一制度的有效实施。     

First- and Second-order Asymptotics for the Tail Distortion Risk Measure of Extreme Risks

The tail distortion risk measure at level p was first introduced in Zhu and Li (2012 Zhu, L., Li, H. (2012). Tail distortion risk and its asymptotic analysis. Insur. Math. Econ. 51(1):115–121.[Crossref], [Web of Science ®] , [Google Scholar]), where the parameter p ∈ (0, 1) indicates the confidence level. They established first-order asymptotics for this risk measure, as p↑1, for the Fréchet case. In this article, we extend their work by establishing both first-order and second-order asymptotics for the Fréchet, Weibull, and Gumbel cases. Numerical studies are also carried out to examine the accuracy of both asymptotics.     

A generalization of Jeffreys' rule for non regular models

ABSTRACT

We propose a generalization of the one-dimensional Jeffreys' rule in order to obtain non informative prior distributions for non regular models, taking into account the comments made by Jeffreys in his article of 1946. These non informatives are parameterization invariant and the Bayesian intervals have good behavior in frequentist inference. In some important cases, we can generate non informative distributions for multi-parameter models with non regular parameters. In non regular models, the Bayesian method offers a satisfactory solution to the inference problem and also avoids the problem that the maximum likelihood estimator has with these models. Finally, we obtain non informative distributions in job-search and deterministic frontier production homogenous models.     

中共三代领导核心对时代问题的认识

建国后中共三代领导核心对时代问题的认识是在曲折中前进和发展的,并在此基础上形成了几个规律性的认识,即党的领导人必须从时代发展的大局出发,对国内外各方面的新趋势、新动向和新挑战开展深入研究,并同时具有对国际国内重大问题进行战略思维的能力。这是为中国改革开放与现代化建设争取一个长期和平的国际环境的思想前提。     

普通高校体育选项课之分层教学与目标教学的有机整合

根据普通高校体育选项课教学大纲的要求,对分层教学组织形式和目标教学法进行了系统研究,认为二者的有机整合可以有效提高普通高校体育教学的效果。分层教学与目标教学有机整合是分层制订分别适合不同高校大学生的教学目标和考核目标,因材施教,因需指导,因层评价和动态组合等,是帮助学生提高体育学习效果的较好方法,能够让学生最大限度地发挥自身潜力,从而促进大学生身心健康的发展,并帮助他们养成终身体育意识和体育习惯。