Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

Kernel Estimation of Rate Function for Recurrent Event Data

Abstract.  Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.     

一阶非线性中立型方程解的渐近性与振动性

本文研究一类具有交系数和多偏差的一阶非线性中立型微分方程解的渐近性与振动性     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Nonresponse weighting adjustment using estimated response probability

To reduce nonresponse bias in sample surveys, a method of nonresponse weighting adjustment is often used which consists of multiplying the sampling weight of the respondent by the inverse of the estimated response probability. The authors examine the asymptotic properties of this estimator. They prove that it is generally more efficient than an estimator which uses the true response probability, provided that the parameters which govern this probability are estimated by maximum likelihood. The authors discuss variance estimation methods that account for the effect of using the estimated response probability; they compare their performances in a small simulation study. They also discuss extensions to the regression estimator.     

中国人口性别结构的区域差异及演变动态分析

人口性别构成是影响人类婚姻、人口再生产的基本因素，也影响国家经济、政治、文化、教育等方面的发展，也是编制经济、文化、教育、科技、卫生、人民生活、劳动、城乡建设等发展规划的重要依据。同时对于中国当前正在进行的和谐社会建设也具有重要意义。利用中国五次人口普查资料及2005年1％人口抽样资料分析了中国总人口性别比演变动态及地理分布特征。表明：（1）中国在历史上是一个性别比偏高的国家，新中国总人口性别比呈下降趋势；（2）1953到2005年，年龄性别比曲线越来越平稳，性别比最高峰值呈现有低龄组向中龄组及高龄组转移的趋势；（3）各省区之间及城乡之间的性别结构差异由大变小；（4）山区性别比高于平原。重工业城市高于其他城市。大城市高于小城市。     

A Multivariate Model for Repeated Failure Time Measurements

A parametric multivariate failure time distribution is derived from a frailty-type model with a particular frailty distribution. It covers as special cases certain distributions which have been used for multivariate survival data in recent years. Some properties of the distribution are derived: its marginal and conditional distributions lie within the parametric family, and association between the component variates can be positive or, to a limited extent, negative. The simple closed form of the survivor function is useful for right-censored data, as occur commonly in survival analysis, and for calculating uniform residuals. Also featured is the distribution of ratios of paired failure times. The model is applied to data from the literature     

Estimation for Continuous Branching Processes

The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels     

中国社会发展水平综合评价研究

一、问题的提出自20世纪90年代以来,人类发展问题已成为当代社会人们研究的重大课题。诚然,人类社会是发展了,但发展的现实世界中还有许多不尽如人意之处。如经济发展了,却带来许多产品生产过剩的问题;人口平均寿命提高了,却又伴随着出现老龄人口的社会保障问题;经济发展的速度     

分位数回归及应用简介

文章介绍了分位数回归法的概念、算法及主流统计软件R和SAS计算时的语法,并通过实例与以普通最小二乘法为基础的线性回归进行了对比,展现了分位数回归的巨大魅力。