ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUE

In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, θ say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ‘θ > θ₁ ’ or ‘θ < θ₁ ’, where θ₁ is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that θ > θ₁ is to replace an estimator, , of θ by the maximum of and θ₁. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality θ > θ₁ , which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint θ > θ₁ , strictly exceed θ₁ except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which is close to θ₁, and more generally produces estimators that respect the constraint in a smooth, realistic fashion.     

西南边疆多民族地区社会动力机制

在推进和谐社会建设的进程中,西南边疆多民族地区社会动力机制运行不断完善,但还存在许多问题：社会发展的经济动力不足,政府的工作存在比较大的改进空间,法律法规的规范力处在较低层次上,社会成员的认知程度和文化需求的现实满足程度还偏低。实现西南边疆多民族地区社会和谐必须把推动社会发展的经济动力、政治动力、文化动力等充分激活,让创造社会价值和财富的源泉充分进发。     

Conditional variance estimation in heteroscedastic regression models

First, we propose a new method for estimating the conditional variance in heteroscedasticity regression models. For heavy tailed innovations, this method is in general more efficient than either of the local linear and local likelihood estimators. Secondly, we apply a variance reduction technique to improve the inference for the conditional variance. The proposed methods are investigated through their asymptotic distributions and numerical performances.     

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

科学发展观指导下的生态文明建设

21世纪的中国,生态文明的建设已经开始,社会主义现代化建设的实质是社会主义生态文明的建设。建设社会主义生态文明需要从经济建设、政治建设、文化建设、社会建设四个大方面去落实,它是全面贯彻和落实科学发展观的主要实践。     

西南边疆多民族地区社会事业的发展

社会事业是为确保社会转型、维护社会稳定、促进社会和谐和人的全面发展所提供的各种公益性支持与服务活动的总和,也是保障社会可持续发展,实现社会公正,维持社会运行和发展的重要活动。在社会转型期,通过加大和改善对西南边疆多民族地区社会事业的投入和建设,提高西南边疆多民族地区公民文化素质,加强公民法制意识,改善公民精神风貌,完善社会安全体系,使西南边疆少数民族文化教育事业有了长足发展,农村医疗卫生事业有了新突破,社会保障事业有了新进展。这在很大程度上促进了西南边疆社会和睦,逐步实现社会公平正义,为社会主义和谐社会的建设提供了基础。     

我国的边疆治理研究

边疆是一个国家特殊的区域,中国古代由于没有确定的边界,所以把王朝国家统治的边缘地带视为边疆,这样的地区也是少数民族生活的区域,所以也被视为民族地区。近代以后,特别是随着民族国家的建立,国家有了确定的边界,因而形成了以边界界定边疆的方式。由此界定的边疆,就是国家邻近边界的地区。中国自古以来都十分重视边疆治理,并取得了巨大的成就。但是,边疆问题的解决不是一劳永逸的,旧有的边疆问题解决了,新的问题还会产生。因此,边疆治理是一个不断常新的过程。今天,中国还面临着发展、稳定和安全三大边疆问题,不仅要进行边疆治理,而且要根据形势的变化对边疆治理进行重构,促进和加强边疆治理。     

The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.     

Multiphase experiments in practice: A look back

Multiphase experiments are introduced and an overview of their design and analysis as it is currently practised is given via an account of their development since 1955 and a literature survey. Methods that are available for designing and analysing them are outlined, with an emphasis on making explicit the role of the model in their design. The availability of software and its use is described in detail. Overall, while multiphase designs have been applied in areas such as plant breeding, plant pathology, greenhouse experimentation, product storage, gene expression studies, and sensory evaluation, their deployment has been limited.     

On generalised estimating equations for vector regression

Generalised estimating equations (GEE) for regression problems with vector‐valued responses are examined. When the response vectors are of mixed type (e.g. continuous–binary response pairs), the GEE approach is a semiparametric alternative to full‐likelihood copula methods, and is closely related to Prentice & Zhao's mean‐covariance estimation equations approach. When the response vectors are of the same type (e.g. measurements on left and right eyes), the GEE approach can be viewed as a ‘plug‐in’ to existing methods, such as the vglm function from the state‐of‐the‐art VGAM package in R. In either scenario, the GEE approach offers asymptotically correct inferences on model parameters regardless of whether the working variance–covariance model is correctly or incorrectly specified. The finite‐sample performance of the method is assessed using simulation studies based on a burn injury dataset and a sorbinil eye trial dataset. The method is applied to data analysis examples using the same two datasets, as well as to a trivariate binary dataset on three plant species in the Hunua ranges of Auckland.