Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.     

Unifying CRM and EWOC designs for phase I cancer clinical trials

The main goal of phase I cancer clinical trials is to determine the highest dose of a new therapy associated with an acceptable level of toxicity for the use in a subsequent phase II trial. The continual reassessment method (CRM) [O’Quigley, J., Pepe, M., Fisher, L., 1990. Continual reassessment method: a practical design for phase I clinical trials in cancer. Biometrics 46, 33–48] and escalation with overdose control (EWOC) [Babb, J., Rogatko, A., Zacks, S., 1998. Cancer phase I clinical trials: efficient dose escalation with overdose control. Statist. Med. 17 (10), 1103–1120] are two model-based designs used for phase I cancer clinical trials. A few modifications of the (original) CRM and EWOC have been made by many authors. In this paper, we show how CRM and EWOC can be unified and present a hybrid design. We study the characteristics of the approach of the hybrid design. The comparisons of the three designs (CRM, EWOC, and the hybrid design) are presented by convergence rates and overdose proportions. The simulation results show that the hybrid design generally has faster convergence rates than EWOC and smaller overdose proportions than CRM, especially when the true maximum tolerated dose (MTD) is above the mid-level of the dose range considered. The performance of these three designs is also evaluated in terms of sensitivity to outliers.     

On construction of asymptotically correct confidence intervals

In this paper we discuss constructing confidence intervals based on asymptotic generalized pivotal quantities (AGPQs). An AGPQ associates a distribution with the corresponding parameter, and then an asymptotically correct confidence interval can be derived directly from this distribution like Bayesian or fiducial interval estimates. We provide two general procedures for constructing AGPQs. We also present several examples to show that AGPQs can yield new confidence intervals with better finite-sample behaviors than traditional methods.     

On the asymptotic distribution of Cook's distance in logistic regression models

It sometimes occurs that one or more components of the data exert a disproportionate influence on the model estimation. We need a reliable tool for identifying such troublesome cases in order to decide either eliminate from the sample, when the data collect was badly realized, or otherwise take care on the use of the model because the results could be affected by such components. Since a measure for detecting influential cases in linear regression setting was proposed by Cook [Detection of influential observations in linear regression, Technometrics 19 (1977), pp. 15–18.], apart from the same measure for other models, several new measures have been suggested as single-case diagnostics. For most of them some cutoff values have been recommended (see [D.A. Belsley, E. Kuh, and R.E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, 2nd ed., John Wiley & Sons, New York, Chichester, Brisban, (2004).], for instance), however the lack of a quantile type cutoff for Cook's statistics has induced the analyst to deal only with index plots as worthy diagnostic tools. Focussed on logistic regression, the aim of this paper is to provide the asymptotic distribution of Cook's distance in order to look for a meaningful cutoff point for detecting influential and leverage observations.     

Cumulative correspondence analysis of ordered categorical data from industrial experiments

Most studies of quality improvement deal with ordered categorical data from industrial experiments. Accounting for the ordering of such data plays an important role in effectively determining the optimal factor level of combination. This paper utilizes the correspondence analysis to develop a procedure to improve the ordered categorical response in a multifactor state system based on Taguchi's statistic. Users may find the proposed procedure in this paper to be attractive because we suggest a simple and also popular statistical tool for graphically identifying the really important factors and determining the levels to improve process quality. A case study for optimizing the polysilicon deposition process in a very large-scale integrated circuit is provided to demonstrate the effectiveness of the proposed procedure.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

数学中化归问题的教学和实践

本文对数学中化归的方法含义,化归的方法要素和核心作了一些理论探索,提出了化归的三条基本途径：（1）向基本模型化归;（2）向特殊模型化归;（3）向低层模型化归。并对化归方法作了教学实践尝试,从熟悉化、简单化、直观化入手提出了化归是一种重要的解决问题的方法。     

《孟子字义疏证》对《孟子》的阐释和创新

戴震《孟子字义疏证》采用经学训诂的形式对义理内容进行建构,在学术思想史上产生了巨大影响。本文对戴震的义理旨趣、考据特征以及对《孟子》的创新阐释及其缺陷作了分析,认为其过度目的性阐释导致了《疏证》在接受方面的诸多困局。戴震义理学表面上对程朱理学持批判立场,但双方在动机、旨趣和义理内容的建构上不具同源性,戴震把程朱理学瑕疵当成程朱理学本身加以攻击,对原始儒意的理解并没有超越宋儒而进行。戴震对于《孟子》的把握仍有未达,但《疏证》所展现出来的批判精神却影响深远。     

马克思主义的幸福观及其中国化何以可能——基于“中国梦”人民幸福内涵的理论渊源及实践价值视角

关于"中国梦"人民幸福内涵的历史渊源及实践价值研究,必然涉及中国化的马克思主义幸福观存在依据和理论形态等问题。马克思主义幸福观中国化何以可能?这一追问实际包含了两个问题:第一,在实际上是否存在马克思主义幸福观,其是否具有合理性。它与现在我们在非严格意义上使用的"马克思幸福观"是否应该有所区别。第二,中国革命为什么需要马克思主义幸福观中国化?这一命题所指称的过程是否真正发生过。科学的马克思主义幸福观,就是符合马克思主义幸福观本来面目和本质特性的关于马克思主义幸福观认知和评价问题上的根本态度与根本观点,应该包括马克思的伦理幸福观、哲学幸福观和人民的现实幸福论。哲学幸福观在马克思主义幸福观中居于核心地位,幸福本质观是马克思主义哲学幸福观的核心内容。幸福首先是一个关于人的本体论问题,不能仅以道德来界定幸福的内涵。实践本体论是马克思主义哲学幸福观产生的母体,将唯心主义的幸福观改造成实践唯物主义的幸福观,将幸福感作为成功的社会实践活动的结果和必要环节。人民的现实幸福论是马克思的幸福本质论革命的主要成果和标志,从关注现实人的幸福本身转向探求人民的现实幸福实现的途径和条件,经历了从劳动幸福观到实践幸福观的过渡。"人民的现实幸福论"具体化、中国化就是马克思主义幸福观中国化的主要内涵和基本路径,"中国特色"人民的现实幸福论是中国特色社会主义幸福理论的基本存在形态及表现形式,是马克思主义幸福观中国化的理论成果之核心内容。"中国梦"蕴含的"人民幸福"思想的理论创新则是"人民幸福本位"思想的不断深化和大众化。