Adaptive confidence intervals of desired length and power for normal means

In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates, in form of confidence intervals on the parameters of interest. The length of a confidence interval characterizes the accuracy of the whole findings. Consequently, confidence intervals should be constructed to hold a desired length. Basic ideas go back to Stein (1945) and Seelbinder (1953) who proposed a two-stage procedure for hypothesis testing about a normal mean. Tukey (1953) additionally considered the probability or power a confidence interval should possess to hold its length within a desired boundary. In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein's concept. Concrete rules for sample size updating are provided. Following an adaptive two-stage design of O’Brien and Fleming (1979) type, a real data example is worked out in detail.     

基于分层贝叶斯分析的残疾率小域估计方法

小域估计（Small Area Estimation）是抽样调查领域里一个重要的研究方向,国计民生中的许多重要问题如失业率、传染病的发病率和民意测验等抽样调查都需要采用不同的小域估计方法。本文针对小域估计问题,以估计方法发展脉络为主线,以分层贝叶斯分析的小域估计为重点,对小域估计问题的理论、方法和最新进展进行简述,并利用澳大利亚残疾、老龄化和护理者（SDAC 2003）抽样调查实际数据,从分层贝叶斯分析角度对澳大利亚残疾率进行估计,最后对估计结果进行比较和讨论。     

否定的逻辑:汶川地震灾区民众的 情感认知冲突及其转换

我们在汶川地震灾区的田野调查中发现,当地人的话语表达充满了思维逻辑上的冲突,而此种冲突所体现出来的一种＂认知失调＂现象又折射出了其背后潜在的＂矛盾情感＂问题,体现了人类认知潜能中＂否定的逻辑＂之规律。在经历一场剧烈的情感与认知＂磨合＂后,当地人逐渐借助某种适应性转换的机制恢复到相对平静的认知状态,但是这种转变是一种同时蕴含着延续与革新两个方面要素的开放性恢复,它印证了灾区社会重建过程中深远的社会与文化变迁。     

Selection buasubg parameters in adaptive ridge regression estimators

Strawderman's family of regression estimators is considered. The choice of the scalars wbich characterize the biasing parameter is studied by obtaining the bias vector and the mean squared error matrix.     

Nonparametric testing of closeness between two unknown distribution functions

Based on the kernel integrated square difference and applying a central limit theorem for degenerate V-statistic proposed by Hall (1984), this paper proposes a consistent nonparametric test of closeness between two unknown density functions under quite mild conditions. We only require the unknown density functions to be bounded and continuous. Monte Carlo simulations show that the proposed tests perform well for moderate sample sizes.     

Asymptotic normality of a weighted integrated squared error of kernel regression estimates with data-dependent bandwidth

Let (X, Y) be a bivariate random vector and let be the regression function of Y on X that has to be estimated from a sample of i.i.d. random vectors (X₁, Y₁),…,(X_n, Y_n) having the same distribution as (X, Y). In the present paper it is shown that the normalized integrated squared error of a kernel estimator with data-driven bandwidth is asymptotically normally distributed.     

Design of a rotation scheme for a stratified multi-stage sample

A rotation scheme for a stratified multi-stage sample, discussed in this paper, was designed to statisfy the following conditions: (i) there is a constraint on the number of units that can be replaced in each round, and (ii) it is relatively inexpensive to increase the sample size gradually. An example of these conditions was observed in the development of a plan for measuring the accuracy of the billing process of a telephone company. Estimators of the population proportion of elements that possess a specified characteristic are also derived. Each estimator is a weighted average of the corresponding estimates based on the retained units from the original sample and on the new units, where the weight of the estimate based on the new units increases over time. While this rotation scheme is discussed in connection with the billing accuracy of a telephone company, the methodology can be applied to other similar problems.     

Posterior robustness with more than one sampling model

In order to robustify posterior inference, besides the use of large classes of priors, it is necessary to consider uncertainty about the sampling model. In this article we suggest that a convenient and simple way to incorporate model robustness is to consider a discrete set of competing sampling models, and combine it with a suitable large class of priors. This set reflects foreseeable departures of the base model, like thinner or heavier tails or asymmetry. We combine the models with different classes of priors that have been proposed in the vast literature on Bayesian robustness with respect to the prior. Also we explore links with the related literature of stable estimation and precise measurement theory, now with more than one model entertained. To these ends it will be necessary to introduce a procedure for model comparison that does not depend on an arbitrary constant or scale. We utilize a recent development on automatic Bayes factors with self-adjusted scale, the ‘intrinsic Bayes factor’ (Berger and Pericchi, Technical Report, 1993).     

Comparison of efficient L- and R-estimators of location

Scholz (1974) proved that the asymptotic variance of an R-estimator of location is no larger than that of an L-estimator when the observations come from a distribution G different from the distribution F for which the two estimators are efficient. This note extends this result to distributions F whose density has a first but no second derivative.     

Large sample theory of the Langevin distribution

The Langevin (or von Mises-Fisher) distribution of random vector x on the unit sphere ω_q in $\text{R}$^q has a density proportional to exp κμ'x where μ'x is the scalar product of x with the unit modal vector μ and κ?0 is a concentration parameter. This paper studies estimation and tests for a wide variety of situations when the sample sizes are large. Geometrically simple test statistics are given for many sample problems even when the populations may have unequal concentration parameters.