大规模数据下基于充分降维的Leverage重要性抽样方法

随着信息技术的飞速发展，大规模数据在短时间内搜集并储存下来，为分析决策提供了巨大的信息量，也给统计建模带来了一定难度。对于样本容量大、变量个数少的数据，Leverage重要性抽样是一个简便可行的方法。本文发现，该方法中度量样本重要性的Leverage分数与因变量无关，而且在维度较大的情形下对样本没有区分程度，使得估计结果较差。为了同时考虑因变量和维度的影响，本文提出了基于充分降维的Leverage重要性抽样方法。该方法以不损失信息为前提，在充分降维的空间内重新计算Leverage分数，使得抽样更具有代表性。模拟数据分析显示，在样本容量较大的复杂数据中，相比于原始的Leverage重要性抽样方法，本文提出的方法可以降低估计的均方误差。三个实际数据也证实了该方法的可行性和有效性。     

Estimating the Number of Change Points in Exponential Families Distributions

A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estimator to maximize some criterion, say SC ( k ), which is to maximize the log- likelihood function with some penalty term, is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simulated results are given, and the Nile problem is investigated by this method.     

Descriptive tests for the identification of outliers in the errors in variables linear model

In this paper the most commonly used diagnostic criteria for the identification of outliers or leverage points in the ordinary regression model are reviewed. Their use in the context of the errors-in-variables (e.v.) linear model is discussed and evidence is given that under the e.v. model assumptions the distinction between outliers and leverage points no longer exists.     

线性拓扑空间中多目标规划的最优性条件

本文引进了Ｓ－有效性的概念，在目标映射为广义锥－次类凸的条件下，在序线性拓扑空间中讨论了多目标规划的Ｌａｇｒａｎｇｅ乘子，鞍点和几个Ｓ－最优性的必要条件，推广了已有的结果。     

完备度量空间中四个映象的公共不动点

利用度量空间中自映象对相容的条件，讨论了完备度量空间中四个映象的公共不动点的存在性，推广和统一了已有文献中的某些结果．     

集值与单值映像的重合点定理

在度量空间与具有W-凸结构的凸度量空间中,讨论了集值与单值映像对重合点的存在性,所得结论推广了有关文献中相应的结论.     

空间的凸性和远达点映射的连续性

本文给出空间严格凸、CLUB和LUR的新特征刻划,后用这些特征对中一定理作了改进.     

STATISTICAL CHALLENGES OF AIDS: (The 1990 Knibbs Lecture, Canberra, 27 November 1990)

Issues that are central to the understanding and management of the HIV epidemic have generated numerous statistical challenges. This paper considers questions concerning the incubation period, the effects of treatments, pre diction of AIDS cases, the choice of surrogate end points for the assessment of treatments and design of strategies for screening blood samples. These issues give rise to a broad range of intriguing problems for statisticians. We describe some of these problems, how they have been tackled so far and what remains to be done. The discussion touches on topical statistical methods such as smoothing, bootstrapping, interval censoring and the ill-posed inverse problem, as well as asking fundamental questions for frequentist statistics.     

Reference points for getting a target in a soccer competition. A probabilistic model with applications to the Spanish and English Premier League

We model the probabilities that a soccer team gets a target, for example, to play the Champions League, the UEFA Europa League or preserve the category. Taking into account the points won until de mth matchday of the competition, when the winter transfer window is closed. We give closed-form expressions for the probabilities of reaching the goals. We also introduce a risk measure which is going to give us the smallest initial points needed to ensure that the probability of getting the target is larger than a given level.     

Living with zombie companies: Do we know where the threat lies?

This paper shows the existence of extreme types of zombie firm, i.e. companies with negative equity that continue to do business despite having lost their entire equity. We explain how these firms are measured and how the riskier ones are defined with different determinants. Using a Spanish sample from 2010 to 2014 an index called the EZIndex is developed that includes four dimensions of the extreme zombie problem: extension, contagion, recovery signs and immediacy. The paper contributes to zombie theory on the one hand by developing a method for ranking zombie firms based on risks and changes over time, and on the other hand by using a log-linear model to detect the riskiest corporate profiles out of all these risky firms. It demonstrates significant implications that need to be considered by the competent authorities not only in terms of their impact as a whole but also in regard to the particular profile of extreme zombie firms: they are less regulated, large and located in regions with large business fabrics.