On the correct regression function (in L2) and its applications when the dimension of the covariate vector is random

We derive the optimal regression function (i.e., the best approximation in the L₂ sense) when the vector of covariates has a random dimension. Furthermore, we consider applications of these results to problems in statistical regression and classification with missing covariates. It will be seen, perhaps surprisingly, that the correct regression function for the case with missing covariates can sometimes perform better than the usual regression function corresponding to the case with no missing covariates. This is because even if some of the covariates are missing, an indicator random variable δ$\delta$, which is always observable, and is equal to 1 if there are no missing values (and 0 otherwise), may have far more information and predictive power about the response variable Y than the missing covariates do. We also propose kernel-based procedures for estimating the correct regression function nonparametrically. As an alternative estimation procedure, we also consider the least-squares method.     

Partitioning large signed two-mode networks: Problems and prospects

While a substantial amount of attention within social network analysis (SNA) has been given to the study of one-mode networks, there is an increasing consideration of two-mode networks. Recent research on signed networks resulted in the relaxed structural balance (RSB) approach and its subsequent extension to signed two-mode networks involving social actors and social objects. We extend this approach to large signed two-mode networks, and address the methodological issues that arise. We develop tools to partition these types of networks and compare them with other approaches using a recently collected dataset of United Nations General Assembly roll call votes. Although our primary purpose is methodological, we take the first step towards bridging Heider's structural balance theory with recent theorizing in international relations on soft balancing of power processes.     

An evaluation of the performance of kernel estimators for graduating mortality data

In the graduation of the age-specific mortality pattern, recent emphasis has been placed on the use of kernel regression estimators. Three such estimators are the Nadaraya-Watson, Gasser-Muller and kernel weighted local linear estimators. This paper discusses the theoretical background of each estimator and evaluates their accuracy in graduating age-specific mortality using data for France, Japan and Sweden. For comparison, we also fit the Heligman-Pollard model and its nine-parameter variant by Kostaki. The Gasser-Muller estimator is found to be superior to the two other kernel estimators in that it is both more stable and not influenced by boundary effects. Furthermore, compared with the two parametrric models, the Gasser-Muller estimator provides a more satisfactory graduation, especially at older adult ages, in terms both of smoothness and of fidelity between the observed and graduated rates.     

柳宗元《晋问》简论

《晋问》具有丰富真实的内容、深刻的思想内涵和高妙的艺术表现力,可谓“七体”成家之作。该文表现了柳宗元雄深雅健的文风,展现了其努力回归汉文并超越汉文的成功。     

关于中国全要素生产率测度的研究——基于一阶差分对数模型和有效资本存量的再测算

本文对以往我国全要素生产率测度中存在的问题做了较为系统的分析,试图总结一套科学且具有可操作性的测度方法。本文在区分实际资本存量和有效资本存量的基础上,根据我国资本存量估算数据,采用一阶差分对数模型和有关经济计量学方法,估计资本与劳动的产出弹性,避免了可能出现的“伪回归”“序列相关”“多重共线性”和“异方差”等问题,从而保证所测度的产出弹性估计值既符合经济理论分析又能通过经济计量学检验。本文还阐述了全要素生产率与广义技术进步这两个指标 的联系与区别,并通过实证分析揭示了不同时期两项指标产生差异的原因。实证分析结果表明,改革开放以来全要素生产率提高对促进我国经济增长发挥了重要作用。     

汉初刘邦分封异姓王原因新探

汉初刘邦分封异姓王不能只归结为刘邦的"不得已而为之",因为任何一个历史事实的出现,必定有其时代的需要,所以应看到当时的文化、政治、经济和军事发展的推动作用。且从刘邦本人及其集团对他的影响来看,刘邦潜意识中也有分封异姓王的想法。     

采用一元辅助信息的多元二相抽样的比估计

一元抽样调查的理论已经发展相对成熟．但实际问题中往往涉及多个指标,一元理论不能满足需要．本文研究了多元二相抽样,并且在多元二相抽样中添加了一元辅助信息。定义了采用一元辅助信息的多元比估计,得到了采用一元辅助信息的多元二相抽样的比估汁量及其性质．并且证明了在满足一定条件时．采用一元辅助信息的多元二相抽样的比估计量优于多元简单随机抽样的简单估计量．     

Multiple change-point estimation with U-statistics

We consider a multiple change-point problem: a finite sequence of independent random variables consists of segments given by a known number of the so-called change-points such that the underlying distribution differs from segment to segment. The task is to estimate these change-points under no further assumptions on the within-segment distributions. In this completely nonparametric framework the proposed estimator is defined as the maximizing point of weighted multivariate U-statistic processes. Under mild moment conditions we prove almost sure convergence and the rate of convergence.     

Estimation of parameters in heavy-tailed distribution when its second order tail parameter is known

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for both first and second order tail parameters. In this work, estimation of parameters in heavy-tailed distributions are studied under the second order regular variation framework when the second order parameter in the distribution tail is known. This is motivated in large part by a recent work by the authors showing that the second order tail parameter is known for a large class of popular random difference equations (for example, ARCH models). The focus is on least squares estimators that generalize rank-based and QQ estimators. Though other possible estimators are also briefly discussed, the least squares estimators are most simple to use and perform best for finite samples in Monte Carlo simulations.     

Proper Bayes minimax estimators of the normal mean matrix with common unknown variances

This paper addresses the problem of estimating a matrix of the normal means, where the variances are unknown but common. The approach to this problem is provided by a hierarchical Bayes modeling for which the first stage prior for the means is matrix-variate normal distribution with mean zero matrix and a covariance structure and the second stage prior for the covariance is similar to Jeffreys’ rule. The resulting hierarchical Bayes estimators relative to the quadratic loss function belong to a class of matricial shrinkage estimators. Certain conditions are obtained for admissibility and minimaxity of the hierarchical Bayes estimators.