On improving convergence rate of Bernstein polynomial density estimator

This paper is concerned with the Bernstein estimator [Vitale, R.A. (1975), ‘A Bernstein Polynomial Approach to Density Function Estimation’, in Statistical Inference and Related Topics, ed. M.L. Puri, 2, New York: Academic Press, pp. 87–99] to estimate a density with support [0, 1]. One of the major contributions of this paper is an application of a multiplicative bias correction [Terrell, G.R., and Scott, D.W. (1980), ‘On Improving Convergence Rates for Nonnegative Kernel Density Estimators’, The Annals of Statistics, 8, 1160–1163], which was originally developed for the standard kernel estimator. Moreover, the renormalised multiplicative bias corrected Bernstein estimator is studied rigorously. The mean squared error (MSE) in the interior and mean integrated squared error of the resulting bias corrected Bernstein estimators as well as the additive bias corrected Bernstein estimator [Leblanc, A. (2010), ‘A Bias-reduced Approach to Density Estimation Using Bernstein Polynomials’, Journal of Nonparametric Statistics, 22, 459–475] are shown to be O(n^?8/9) when the underlying density has a fourth-order derivative, where n is the sample size. The condition under which the MSE near the boundary is O(n^?8/9) is also discussed. Finally, numerical studies based on both simulated and real data sets are presented.     

额尔金眼中的太平天国

1858年额尔金访华,在清政府的许可下游历长江流域,此时正值太平天国与英国方面再度进行外交接触之际。在大叙事结构的背景下,额尔金的书信、日记记录了当时双方的真实交互。以此为切入点,可以更加清楚地看到太平天国作为一个政治主体,在1858~1861年间其官方外交手段是如何失败的。     

基于利益视角的“新农保”政策过程分析——以民族地区为例

基于公共政策的利益视角,以民族地区为例,分析了新农保政策实施过程中可能出现的居民家庭、集体、地方政府和中央政府等多维利益主体之间的利益矛盾,并进一步探讨新农保政策利益主体与利益客体的利益运动过程。在此基础上充分利用公共管理工具,在促进经济发展的宏观环境下应对新农保政策的适应性调整。     

An Optimal Confidence Region for the Largest and the Smallest Means from a Multivariate Normal Distribution

An optimal confidence region is proposed for obtaining the largest and the smallest means of a multivariate normal distribution with a common unknown variance and a non-negative correlation coefficient. The confidence region is compared to a class of asymmetric confidence regions, and the results show that it is uniformly better. Further, a design-oriented two-stage confidence region with a fixed width is also given. Finally, the optimal confidence region is applied to an experiment to measure the treatment effectiveness of a physical therapy with four independent groups and the result reveals that the proposed confidence region can provide some useful information.     

Tail density estimation for exploratory data analysis using kernel methods

It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models.     

Growth of tuber crops and almost sure band for quantiles

Some tuber crops are governed by memoryless property of exponential distribution leading to a mixture distribution with heavy tail. Quantile-based estimators may then be appropriate than mean as a measure of central tendency. We prove almost sure representation theorems for sample quantiles in a general setup of U statistics, under slightly stronger assumption than assuming the existence of a continuously differentiable distribution function F for the kernel h. We obtain almost sure (a.s.) upper and lower estimate for F^{? 1}(p), p ∈ (0, 1) as a band for p varying. As an application, dataset arising from two varieties of potato cultivation are analyzed.     

The Experience of Using Poverty Alleviation with Characteristic Industries in the Region of the Panzhihua-Xichang-Taking Miyi County of Panzhihua as a Case Study

Miyi county lies along the southeast edge of Qinghai - Tibetan plateau. It is in the southwest corner of Sichuan province,to the north￣east of Panzhihua,and lies at the intersection of the Yalong River...     

Randomized quantile regression estimation for heteroskedastic non parametric model

In this paper, we propose robust randomized quantile regression estimators for the mean and (condition) variance functions of the popular heteroskedastic non parametric regression model. Unlike classical approaches which consider quantile as a fixed quantity, our method treats quantile as a uniformly distributed random variable. Our proposed method can be employed to estimate the error distribution, which could significantly improve prediction results. An automatic bandwidth selection scheme will be discussed. Asymptotic properties and relative efficiencies of the proposed estimators are investigated. Our empirical results show that the proposed estimators work well even for random errors with infinite variances. Various numerical simulations and two real data examples are used to demonstrate our methodologies.     

A weighted least-squares cross-validation bandwidth selector for kernel density estimation

Since the late 1980s, several methods have been considered in the literature to reduce the sample variability of the least-squares cross-validation bandwidth selector for kernel density estimation. In this article, a weighted version of this classical method is proposed and its asymptotic and finite-sample behavior is studied. The simulation results attest that the weighted cross-validation bandwidth performs quite well, presenting a better finite-sample performance than the standard cross-validation method for “easy-to-estimate” densities, and retaining the good finite-sample performance of the standard cross-validation method for “hard-to-estimate” ones.     

西部地区学校课程建设中存在的问题与对策思考

文章对西部地区学校课程建设中遇到的困难与问题从认识、制度、条件三个层面进行了分析,并就学校课程建设提出具体建议：学校应以实践—评估—开发为基本策略,对自身所做过的工作进行全面反思和总结,抓住主要环节,重点突破。同时,学校要争取高校和学术机构的支持,开展扎实有效的培训活动,教育行政部门要提升课程领导的能力,进行知识管理。