On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

浅论诚信友爱是构建社会主义和谐社会的道德基础

诚信友爱，是和谐社会的六个基本特征之一，是现代人际关系的一种理想状态，是构建社会主义和谐社会的道德基础。一个社会能否和谐，一个国家能否长治久安，很大程度上取决于全体社会成员的诚信友爱的道德素质水平。本文从正确把握诚信友爱的内涵、诚信友爱在构建社会主义和谐社会中所起的作用及现存的问题等方面进行分析，提出具体的措施方法，对构建社会主义和谐社会具有一定的现实意义。     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

水资源跨流域配置的经济学分析

由于我国水资源空间分布不均匀的突出特点 ,大型跨流域调水工程已经成为我国国民经济可持续发展的重要支撑。文章从水资源的经济特点出发 ,结合南水北调中线工程 ,对水资源跨流域配置的市场供求、成本收益等资源经济学问题进行了分析 ,并对社会主义市场经济条件下水资源跨流域配置的利益分配机制进行了探讨     

A note on LeCam’s bound for the distance between the Poisson binomial and the Poisson distribution

n possibly different success probabilities p ₁, p ₂, ..., p _n is frequently approximated by a Poisson distribution with parameter λ = p ₁ + p ₂ + ... + p _n . LeCam's bound p ² ₁ + p ² ₂ + ... + p _n ² for the total variation distance between both distributions is particularly useful provided the success probabilities are small. The paper presents an improved version of LeCam's bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution. Received: May 10, 2000; revised version: January 15, 2001     

随机变量投影的一种应用

利用随机变量的投影关系,定义了偏方差矩阵,从而导出了逆方差阵元素的一种形式在随机变量是正态的条件,它为判别条件独立性有方便的操作办法。     

用Powell法求颗粒尺寸分布

本文用最优化理论中的Powell直接法求激光粒度仪中的颗粒尺寸分布。数值模拟及对标准颗粒的实测表明,该算法的计算精度高,能较好地解决粒度仪通常存在的计算结果随初始设定值变化的多值性问题。     

论社会主义新经济伦理道德规范的建构

随着我国的改革开放和社会主义市场经济的发展,经济生活中的“越轨”和“失范”现象日渐突出,因此,构建社会主义新经济伦理道德规范具有重要性、必然性;其建构原则是:社会主义市场经济的内在要求,“三个有利于”的评价尺度,承前启后的传统要求;其具体内容包括共同富裕、自立自主、互利互惠、劳动责任感、开拓进取等８个方面的内容。     

In Memoriam: Emeritus Professor Henry Oliver Lancaster, AO FAA 1 February 1913 – 2 December 2001

The death, in Sydney, of Oliver Lancaster marks the end of an era in the histories of the Statistical Society of Australia, which (in its previous existence as the Statistical Society of New South Wales) he helped found in 1947, and of the Australian Journal of Statistics of which he was founding editor (1959–1971). Oliver Lancaster was Foundation Professor of Mathematical Statistics at the University of Sydney (1959–1978), where he spent his life as student and academic. During his academic career, he achieved scholarly distinction in at least four fields: mathematical statistics, medical and public health statistics, the history of medicine and of statistics, and statistical bibliography. With E.J.G. Pitman (1897–1993), M.H. Belz (1897–1975), E.A. Cornish (1909–1973) and P.A.P. Moran (1917–1988) he was part of a cohort of renowned Australian mathematical statisticians who laid the foundation of the glory days of Australian mathematical statistics. This obituary and tribute focuses on some of these aspects, within a broader historical picture.     

Confidence Intervals for Current Status Data

Abstract.  The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio-based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio-based intervals are preferable from several perspectives.