Asymptotic optimality of a two-stage procedure in Bayes sequential estimation

The problem of sequential estimation of the mean with quadratic loss and fixed cost per observation is considered within the Bayesian framework. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem. The proposed two-stage procedure is robust in the sense that it does not depend on the distribution of outcome variables and the prior. It is shown to be asymptotically not worse than the optimal fixed-sample-size procedures for the arbitrary distributions, and to be asymptotically Bayes for the distributions of one-parameter exponential family.     

Robust small area estimation

Small area estimation has received considerable attention in recent years because of growing demand for small area statistics. Basic area‐level and unit‐level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of small area means. Although this classical method is useful for estimating the small area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop areas for counties in Iowa, using farm‐interview data on crop areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada     

An Adaptive Two-stage Estimation Method for Additive Models

Abstract.  In this paper, a two-stage estimation method for non-parametric additive models is investigated. Differing from Horowitz and Mammen's two-stage estimation, our first-stage estimators are designed not only for dimension reduction but also as initial approximations to all of the additive components. The second-stage estimators are obtained by using one-dimensional non-parametric techniques to refine the first-stage ones. From this procedure, we can reveal a relationship between the regression function spaces and convergence rate, and then provide estimators that are optimal in the sense that, better than the usual one-dimensional mean-squared error (MSE) of the order n ^−4/5 , the MSE of the order n ^{− 1} can be achieved when the underlying models are actually parametric. This shows that our estimation procedure is adaptive in a certain sense. Also it is proved that the bandwidth that is selected by cross-validation depends only on one-dimensional kernel estimation and maintains the asymptotic optimality. Simulation studies show that the new estimators of the regression function and all components outperform the existing estimators, and their behaviours are often similar to that of the oracle estimator.     

Sir Godfrey Thomson: a statistical pioneer

Summary.  Godfrey Thomson (1881–1955) was a leading figure in intelligence testing who made his name in that field first at Armstrong College, Newcastle, and then at the University of Edinburgh. In the course of his practical work he identified many theoretical problems which were essentially statistical in character. In particular, he used maximum likelihood estimation as early as 1919 and his statistical work largely set the course of modern factor analysis and related techniques. His statistical abilities were recognized, at different stages of his career, by both Karl Pearson and Sir Ronald Fisher. His key insight was to recognize the importance of Fisherian inference for the future of that subject.     

An efficient two-stage randomized response model under stratified random sampling

A two-stage randomized response model is extended to stratified random sampling in order to find out more efficient estimators of proportions built from sensitive questions, which respondents may not answer truthfully, in a population divided into homogeneous subgroups. In each subgroup, the respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating “yes” or “no”. In the latter case, they are required to report the outcome. Such extension provides a more efficient estimator of the proportion of the population having a given sensitive attribute than its counterpart in simple random sampling. The extended two-stage randomized response model is more efficient than the stratified randomized response model, where respondents must answer the sensitive question either in the first or in the second stage. Moreover, it increases the respondents’ cooperation. When strata weights are unknown, they are estimated by the double sampling method.     

我国林木生物质能源资源分类及总量估算

林木生物质能源具有很大的开发价值和利用潜力。目前我国林木生物质能源的发展尚处于起步阶段,资源分类及资源量的估计方法也有待统一和完善。基于对林木生物质能源资源的概念界定及其主要来源,对林木生物质能源资源进行分类,并采用自下而上的估计方法,结合我国最新的森林资源清查数据,分析林木生物质能源资源各组成部分的资源量和可利用情况。     

中国高技术产业技术创新效率动态演进

基于2013—2017年中国28个省（区、市）高技术产业的面板数据,在以增强型罗素测量模型测度高技术产业技术创新效率的基础上,运用核密度估计和泰尔指数对效率进行系统分析。结果表明：中国高技术产业技术创新活动的综合效率处于较低水平;纯技术效率呈东、中、西和东北阶梯下降,规模效率呈东北、西、中和东阶梯下降;综合效率总体分布密度曲线随时间右移且右拖尾特征明显;区域内部效率差异是造成地区间效率差异的主要原因;纯技术效率和规模效率在统计上显著负相关;样本期间,高技术产业技术创新活动整体规模报酬不佳,每年处于规模报酬递减的地区数超过50%。基于分析结果,给出相应政策建议。     

论当代中国先进文化的判断标准

当代中国先进文化是指“中国特色社会主义文化”或“社会主义精神文明”,它是与“落后文化”、“腐朽文化”相对而言的。其判断标准有以下方面:是否能够促进社会主义社会的生产力发展;是否能够体现最广大人民群众的根本利益的要求;是否能够促进人的全面发展;是否能够站在时代前列,反映人民群众的意志和愿望,表达人民群众的心声,在改革开放和现代化建设中有着强大的号召力、吸引力和凝聚力;是否能够不断丰富人们的精神世界、满足人们的精神需求,对社会有着巨大的整合作用。     

Efficient estimators with categorical ranked set samples: estimation procedures for osteoporosis

Ranked set sampling (RSS) design as a cost-effective sampling is a powerful tool in situations where measuring the variable of interest is costly and time-consuming; however, ranking information about sampling units can be obtained easily through inexpensive and easy to measure characteristics at little or no cost. In this paper, we study RSS data for analysis of an ordinal population. First, we compare the problem of non-representative extreme samples under RSS and commonly-used simple random sampling. Using RSS data with tie information, we propose non-parametric and maximum likelihood estimators for population parameters. Through extensive numerical studies, we investigate the effect of various factors including ranking ability, tie generating mechanisms, the number of categories and population setting on the performance of the estimators. Finally, we apply the proposed methods to the bone disorder data to estimate the proportions of patients with osteopenia and osteoporosis status.