Umvu estimators for the population mean and variance based on random effects models for lognormal data

Cross-classified data are often obtained in controlled experimental situations and in epidemiologic studies. As an example of the latter, occupational health studies sometimes require personal exposure measurements on a random sample of workers from one or more job groups, in one or more plant locations, on several different sampling dates. Because the marginal distributions of exposure data from such studies are generally right-skewed and well-approximated as lognormal, researchers in this area often consider the use of ANOVA models after a logarithmic transformation. While it is then of interest to estimate original-scale population parameters (e.g., the overall mean and variance), standard candidates such as maximum likelihood estimators (MLEs) can be unstable and highly biased. Uniformly minimum variance unbiased (UMVU) cstiniators offer a viable alternative, and are adaptable to sampling schemes that are typiral of experimental or epidemiologic studies. In this paper, we provide UMVU estimators for the mean and variance under two random effects ANOVA models for logtransformed data. We illustrate substantial mean squared error gains relative to the MLE when estimating the mean under a one-way classification. We illustrate that the results can readily be extended to encompass a useful class of purely random effects models, provided that the study data are balanced.     

LIMIT THEOREMS FOR ASYMPTOTICALLY MINIMAX ESTIMATION OF A DISTRIBUTION WITH INCREASING FAILURE RATE UNDER A RANDOM MIXED CENSORSHIP/TRUNCATION MODEL

ABSTRACT

The search for optimal non-parametric estimates of the cumulative distribution and hazard functions under order constraints inspired at least two earlier classic papers in mathematical statistics: those of Kiefer and Wolfowitz[1] Kiefer, J. and Wolfowitz, J. 1976. Asymptotically Minimax Estimation of Concave and Convex Distribution Functions. Z. Wahrsch. Verw. Gebiete, 34: 73–85. [Crossref], [Web of Science ®] , [Google Scholar] and Grenander[2] Grenander, U. 1956. On the Theory of Mortality Measurement. Part II. Scand. Aktuarietidskrift J., 39: 125–153.  [Google Scholar] respectively. In both cases, either the greatest convex minorant or the least concave majorant played a fundamental role. Based on Kiefer and Wolfowitz's work, Wang3-4 Wang, J.L. 1986. Asymptotically Minimax Estimators for Distributions with Increasing Failure Rate. Ann. Statist., 14: 1113–1131. Wang, J.L. 1987. Estimators of a Distribution Function with Increasing Failure Rate Average. J. Statist. Plann. Inference, 16: 415–427.   found asymptotically minimax estimates of the distribution function F and its cumulative hazard function Λ in the class of all increasing failure rate (IFR) and all increasing failure rate average (IFRA) distributions. In this paper, we will prove limit theorems which extend Wang's asymptotic results to the mixed censorship/truncation model as well as provide some other relevant results. The methods are illustrated on the Channing House data, originally analysed by Hyde.5-6 Hyde, J. 1977. Testing Survival Under Right Censoring and Left Truncation. Biometrika, 64: 225–230. Hyde, J. 1980. “Survival Analysis with Incomplete Observations”. In Biostatistics Casebook 31–46. New York: Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics.       

A Comparison of Three-level Orthogonal Arrays in the Presence of a Possible Correlation in Observations

When we want to compare two designs we usually assume the standard linear model with uncorrelated observations. In this paper we use the comparison method proposed by Ghosh & Shen (2006) to compare three level orthogonal arrays with 18, 27 and 36 runs under a possible presence of correlation in observations.     

Random Bernstein Polynomials

Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a Bernstein–Dirichlet prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a changing dimension parameter space.     

The robustness of the quasilikelihood estimator

The quasilikelihood estimator is widely used in data analysis where a likelihood is not available. We illustrate that with a given variance function it is not only conservative, in minimizing a maximum risk, but also robust against a possible misspecification of either the likelihood or cumulants of the model. In examples it is compared with estimators based on maximum likelihood and quadratic estimating functions.     

健全我国政府经济职能体系的若干思考

完善我国政府经济职能体系不仅与经济体制改革密切相关,也为和谐社会的构建提供重要保障。我国政府经济职能有个演变的过程,目前的体系在经济调节、市场监管、社会管理、公共服务等方面存在问题,从这四个方面初步探讨健全我国政府经济职能体系的基本思路。     

氢化物发生-原子荧光光谱法测定奶粉中砷含量的不确定度评定

介绍氢化物发生-原子荧光光谱法测定奶粉中砷含量的不确定度评定方法[1][2]。从测量各步骤评定了不确定度的各项来源[3],对该方法所得分析结果的已识别来源的不确定度影响进行评价。并且可为实验室在该检测过程中进一步提高检测数据的可靠性和一致性作参考。     

农村税费改革的调研及新举措

农村税费改革是一项十分复杂的工作 ,涉及各方面利益 ,是农村分配关系的一次重大调整。安徽省试行农村税费改革以来 ,取得了明显的成绩 ,但也暴露出更深层次的问题。本文详细介绍了农村税费改革的内涵 ,具体分析了我国农村税费改革中存在的问题 ,在此基础上提出了具体的应对策略。     

论政党价值观的功能本

政党价值观的功能主要包括显功能和潜功能,显功能又包括正功能和反功能两个方面.政党价值观的正功能,是政党价值观对于政党成员、政党组织乃至整个社会所具有的积极功能,主要表现为合法性辩护、凝聚激励、价值导向和社会整合等功能.政党价值观的反功能,是指政党价值观对政党的生存和发展乃至整个社会产生的消极作用和不良影响,集中体现在错误或落后的价值观的不良影响之中.不为政党成员和广大民众所预期而又确实地对政党乃至社会产生直接或间接影响的一切社会作用或客观结果,便是政党价值观的潜功能.这种结果可能与政党及其成员的主观目的相一致,也可能出现不一致的情况.     

政府的权力作用方式变革与社会治理能力提升

伴随十八届三中全会全面深化改革的启动,以"转变政府职能"为核心的行政体制改革对政府变革权力作用方式,推进治理体系和治理能力现代化提出了新要求。回溯建国以来政府权力作用方式的演变与适应社会治理需要之间的互动过程可以发现,随着社会治理主体、治理方式、治理理念的变化,政府权力作用方式需要相应变革以适应现代社会治理的需要。因此着重探讨新形势下的社会治理所要求的政府权力作用方式变革,进而通过变革提升其社会治理能力。