ON THE COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN REGRESSION AFTER VARIABLE SELECTION

This paper considers a linear regression model with regression parameter vector β. The parameter of interest is θ= a^Tβ where a is specified. When, as a first step, a data‐based variable selection (e.g. minimum Akaike information criterion) is used to select a model, it is common statistical practice to then carry out inference about θ, using the same data, based on the (false) assumption that the selected model had been provided a priori. The paper considers a confidence interval for θ with nominal coverage 1 ‐ α constructed on this (false) assumption, and calls this the naive 1 ‐ α confidence interval. The minimum coverage probability of this confidence interval can be calculated for simple variable selection procedures involving only a single variable. However, the kinds of variable selection procedures used in practice are typically much more complicated. For the real‐life data presented in this paper, there are 20 variables each of which is to be either included or not, leading to 2²⁰ different models. The coverage probability at any given value of the parameters provides an upper bound on the minimum coverage probability of the naive confidence interval. This paper derives a new Monte Carlo simulation estimator of the coverage probability, which uses conditioning for variance reduction. For these real‐life data, the gain in efficiency of this Monte Carlo simulation due to conditioning ranged from 2 to 6. The paper also presents a simple one‐dimensional search strategy for parameter values at which the coverage probability is relatively small. For these real‐life data, this search leads to parameter values for which the coverage probability of the naive 0.95 confidence interval is 0.79 for variable selection using the Akaike information criterion and 0.70 for variable selection using Bayes information criterion, showing that these confidence intervals are completely inadequate.     

清代文化政策对八股文衡文标准的影响

“清真雅正”是清代科举八股文的衡文标准。“清真”主要针对理而言,“雅正”针对辞而言。此标准机械而灵活,且具有相当的黜落功能。这一标准有关文风,但它的确立非全因文体发展的内在客观要求而定。它是清初统治者鉴于明末制艺流弊,为配合文化政策的实施而提出的,反映了官方的人才价值取向。这一标准到乾隆时被确定下来,并为满清后来各王朝沿袭并得到强化。     

基于非线性主成分和聚类分析的综合评价方法

针对传统主成分在处理非线性问题上的不足，阐述了传统方法在数据无量纲化中“中心标准化”的缺点和处理“线性”数据时的缺陷，给出了数据无量纲化和处理“非线性”数据时的改进方法，并建立了一种基于“对数中心化”的非线性主成分分析和聚类分析的新的综合评价方法。实验表明，该方法能有效地处理非线性数据。     

论普通话水平测试中异读词的规范问题

普通话水平测试(PSC)中异读词的存在,相当程度上影响了PSC的顺利进行。针对PSC中异读词读音混乱现象,对此类异读词进行系统分类,综合考虑审音标准,提出切实可行的解决办法,有利于确保PSC的科学性、规范性、权威性。     

Bayesian binary segmentation procedure for detecting streakiness in sports

Summary.  When an individual player or team enjoys periods of good form, and when these occur, is a widely observed phenomenon typically called 'streakiness'. It is interesting to assess which team is a streaky team, or who is a streaky player in sports. Such competitors might have a large number of successes during some periods and few or no successes during other periods. Thus, their success rate is not constant over time. We provide a Bayesian binary segmentation procedure for locating changepoints and the associated success rates simultaneously for these competitors. The procedure is based on a series of nested hypothesis tests each using the Bayes factor or the Bayesian information criterion. At each stage, we only need to compare a model with one changepoint with a model based on a constant success rate. Thus, the method circumvents the computational complexity that we would normally face in problems with an unknown number of changepoints. We apply the procedure to data corresponding to sports teams and players from basketball, golf and baseball.     

邓小平“实事求是”思想的当代诠释

邓小平把"一切从实际出发"与"实事求是"并列,这里的"实际"、"实事"要理解为"事实",并且事实具有直接性和可靠性,由此"一切从实际出发"、尊重事实是"实事求是"的出发点。事实包括客体事实和价值事实,价值事实在"实事求是"中更为重要。从价值事实中求"是",这个"是"就集中体现为"三个有利于"标准,"三个有利于"标准是"实事求是"的最终标准。人民利益标准是"三个有利于"标准中的最高标准。由此人民利益标准就成为"实事求是"的最高标准中的核心。人民利益标准既是"实事求是"的最高标准,又是"党的一切执政活动的最高标准",因而就成为中国社会主义现代化建设的最高标准的核心。只有坚持人民利益标准,才能真正实现中华民族的伟大复兴。     

论公司高管职务犯罪行为

职务性是公司高管职务犯罪行为的本质特征;根据不同的划分标准,公司高管职务犯罪行为可以分为几种不同的类型;我国《刑法》对公司高管职务行为的入罪标准作出了不同规定,正确界定公司高管职务犯罪行为与公司犯罪行为之间的区别与联系非常重要。     

民主革命时期毛泽东保护和发展私营经济思想论析

在民主革命时期,毛泽东同志根据中国经济落后的现实国情和中国革命的性质、任务,提出了利用、保护和发展私营经济的思想.这既是对我党历史经验的凝重总结,也是对中国社会政治经济走向的深层思考.这一认识过程的曲折反复也折射出探索中国革命道路的复杂与艰辛.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.     

Akaike Information Criterion for Selecting Variables in the Nested Error Regression Model

The Akaike Information Criterion (AIC) is developed for selecting the variables of the nested error regression model where an unobservable random effect is present. Using the idea of decomposing the likelihood into two parts of “within” and “between” analysis of variance, we derive the AIC when the number of groups is large and the ratio of the variances of the random effects and the random errors is an unknown parameter. The proposed AIC is compared, using simulation, with Mallows' C _p , Akaike's AIC, and Sugiura's exact AIC. Based on the rates of selecting the true model, it is shown that the proposed AIC performs better.