SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.     

Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

Abstract

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald’s development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts.     

Quasi-minimax estimation in the partial linear model

This article discusses the minimax estimator in partial linear model y = Zβ + f + ε under ellipsoidal restrictions on the parameter space and quadratic loss function. The superiority of the minimax estimator over the two-step estimator is studied in the mean squared error matrix criterion.     

全面建设小康社会与加快民族地区发展

民族地区地域广大 ,资源丰富 ,潜在市场广阔 ,在全面建设小康社会中具有十分重要的战略地位。同时 ,民族地区经济社会发展的滞后又给全面建设小康社会带来了许多困难。只有切实克服这些困难和问题 ,才能有效地推进全面建设小康社会的伟大事业。应加大国家的扶持力度 ,认真贯彻党的民族政策 ,解放思想 ,发挥优势 ,依靠科技进步 ,采取一系列措施 ,实现民族地区的跨越式发展。     

跨跃式发展是黑龙江省民族地区全面建设小康社会的关键

本文在分析黑龙江省民族地区社会经济发展存在的差距基础之上,提出跨跃式发展是黑龙江省实现全面建设小康社会的关键,同时就促使民族地区社会经济跨跃式发展阐述了自己的看法。     

论我国民族地区的跨越式发展

跨越式发展是民族发展的一种形式,也是加快我国民族地区经济文化发展的有效途径。文章结合我国国情,分析了我国民族地区要实现跨越式发展的原因和条件,并提出了具体措施和建议。     

Quasi-minimax estimation in the general linear regression model

This paper is mainly concerned with minimax estimation in the general linear regression model y=Xβ+ε$y=X\beta +\epsilon$ under ellipsoidal restrictions on the parameter space and quadratic loss function. We confine ourselves to estimators that are linear in the response vector y  . The minimax estimators of the regression coefficient β$\beta$ are derived under homogeneous condition and heterogeneous condition, respectively. Furthermore, these obtained estimators are the ridge-type estimators and mean dispersion error (MDE) superior to the best linear unbiased estimator b=(X^′W^-1X)^-1X^′W^-1y$b=(X^{\prime }{W}^{-1}X{)}^{-1}{X}^{\prime }{W}^{-1}y$ under some conditions.