Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.     

Recent and classical goodness-of-fit tests for the Poisson distribution

We give a critical synopsis of classical and recent tests for Poissonity, our emphasis being on procedures which are consistent against general alternatives. Two classes of weighted Cramér–von Mises type test statistics, based on the empirical probability generating function process, are studied in more detail. Both of them generalize already known test statistics by introducing a weighting parameter, thus providing more flexibility with regard to power against specific alternatives. In both cases, we prove convergence in distribution of the statistics under the null hypothesis in the setting of a triangular array of rowwise independent and identically distributed random variables as well as consistency of the corresponding test against general alternatives. Therefore, a sound theoretical basis is provided for the parametric bootstrap procedure, which is applied to obtain critical values in a large-scale simulation study. Each of the tests considered in this study, when implemented via the parametric bootstrap method, maintains a nominal level of significance very closely, even for small sample sizes. The procedures are applied to four well-known data sets.     

When Passion Leads to Problematic Outcomes: A Look at Gambling

Vallerand et al. (2003) have proposed that individuals can have two distinct types of passion toward an activity. Harmonious passion, an internal force leading one to choose to engage in the activity, is proposed to be associated with positive consequences. Obsessive passion, an internal pressure forcing one to engage in an activity, is posited to be associated with negative consequences. The present study sought to determine the role of the two types of passion in various cognitive and affective states associated with dependence and problems with gambling. Participants (n = 412) were recruited at the Montréal Casino and given a questionnaire measuring passion toward gambling, as well as consequences associated with dependence and problem gambling. Results showed that obsessive passion for gambling predicted poorer vitality and concentration in daily tasks, as well as increased rumination, anxiety, negative mood, guilt, and problem gambling. These relations were not found for harmonious passion for gambling. Results are discussed in light of the motivational approach to passion (Vallerand et al., 2003).     

Data depth and correlation

Summary: We describe depth–based graphical displays that show the interdependence of multivariate distributions. The plots involve one–dimensional curves or bivariate scatterplots, so they are easier to interpret than correlation matrices. The correlation curve, modelled on the scale curve of Liu et al. (1999), compares the volume of the observed central regions with the volume under independence. The correlation DD–plot is the scatterplot of depth values under a reference distribution against depth values under independence. The area of the plot gives a measure of distance from independence. Correlation curve and DD-plot require an independence model as a baseline: Besides classical parametric specifications, a nonparametric estimator, derived from the randomization principle, is used. Combining data depth and the notion of quadrant dependence, quadrant correlation trajectories are obtained which allow simultaneous representation of subsets of variables. The properties of the plots for the multivariate normal distribution are investigated. Some real data examples are illustrated. *This work was completed with the support of Ca Foscari University.     

相关性下的银行风险集成研究综述

银行风险之间的相关关系会使风险之间相互转化，相互影响，令风险呈现出放大或者缩小的趋势，显著影响着银行风险度量结果的准确性。银行风险集成致力于在充分考虑银行风险相关关系的基础上，对银行风险进行较为准确的度量。但是银行风险具有相关关系种类繁多、表现形式复杂、以及数据的可获得性差等显著特征，导致银行风险的集成度量领域存在诸多挑战。本文对相关性下的银行风险集成研究进行综述，具体从集成对象、集成方法和集成数据三个层次系统展开。首先对银行风险及其蕴含的种类繁多的相关关系类型进行解析，然后分析银行风险相关关系表征出的多种复杂特性，根据对这些特性的刻画能力对银行风险的集成方法进行划分和比较，最后总结了获取银行风险集成数据的多种途径。在此基础上，进一步分析了银行风险集成研究的难点和未来趋势。     

算子的型与指标选择

本文定义了弱*(p,q)型算子,并且通过对强(p,q)型算子指标选择结论的推广,得到了弱(p,q)型算子以及弱*(p,q)型算子指标选择的结论。     

Modelling two way contingency tables with recursive logits and odds ratios

In this work a new type of logits and odds ratios, which includes as special cases the continuation and the reverse-continuation logits and odds ratios, are defined. We prove that these logits and odds ratios define a parameterization of the joint probabilities of a two way contingency table. The problem of testing equality and inequality constraints on these logits and odds ratios is examined with particular regard to two new hypotheses of monotone dependence. Work partially supported by a MIUR2004 grant. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Torino, 2006.     

向量的线性相关性与线性无关性在平面和空间上的几何解释

本文主要阐述向量的线性相关性与线性无关性在平面和空间上的几何解释.     

ASYMPTOTIC EFFICIENCY OF THE BLEST‐TYPE TESTS FOR INDEPENDENCE

Blest (2000, Aust. N. Z. J. Stat. 42 , 101–111) proposed a new measure of rank correlation that is sensitive to discrepancies in the small ranks. This paper investigates the efficiency properties of non‐parametric tests for independence based on Blest's correlation coefficient and its modifications. Pitman efficiency comparisons are made with analogous tests existing in the literature. Conditions for Pitman optimality of the Blest‐type tests are established.