Nonconglomerative coherent conditional probabilities in statistical inference

Noteworthy connections among conglomerability, countable additivity and coherence are discussed in detail, reaching the conclusion that nonconglomerable conditional probabilities must not be doomed and play a significant role in statistical inference. Extended and updated version of a contributed paper presented at the International Conference on “Information Processing and Management of Uncertainty in knowledge-based systems”, IPMU 2004, Perugia, Italy.     

A Discrete Variable Chain Graph for Applicants for Credit

A bank offering unsecured personal loans may be interested in several related outcome variables, including defaulting on the repayments, early repayment or failing to take up an offered loan. Current predictive models used by banks typically consider such variables individually. However, the fact that they are related to each other, and to many interrelated potential predictor variables, suggests that graphical models may provide an attractive alternative solution. We developed such a model for a data set of 15 variables measured on a set of 14 000 applications for unsecured personal loans. The resulting global model of behaviour enabled us to identify several previously unsuspected relationships of considerable interest to the bank. For example, we discovered important but obscure relationships between taking out insurance, prior delinquency with a credit card and delinquency with the loan.     

Likelihood Factorizations for Mixed Discrete and Continuous Variables

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.     

A Nonparametric Test for the Parallelism of Two First-Order Autoregressive Processes

A nonparametric testing procedure for the parallelism of two first-order autoregressive processes is presented. This paper discuss the Mann–Whitney statistic, its natural competitor two-sample t -test, and the bootstrap method. It studies the asymptotic efficacies of the studentized Mann–Whitney statistic and the t -test statistic with their relative efficiency. Simulation results for comparing the powers of these test statistics are also presented.     

Rank tests in the two-sample scale problem with unequal and unknown locations

The two-sample scale problem is studied in the case of unequal and unknown location parameters. The method proposed is based on the idea of Moses (1963) and it is distribution-free. The two samples are separated into random subgroups of the same sizek. It is proposed to choosek=4 and to apply the Wilconxon test or the Savage test to the ranges or sample variances of the subgroups. The asymptotic power functions of the tests are compared. For small and moderate sample sizes simulations are carried out. Relations to some other procedures, especially to the method of Compagnone and Denker (1996) are briefly discussed.     

中国居民收入分布专题实证研究——居民收入分布变迁测度及其影响因素分解

基于核密度估计方法,给出居民收入分布变迁测度及其影响因素分解的相对收入分布方法。使用中国健康和营养调查的微观居民收入数据,实证分析中国居民收入分布及其变迁的特征、过程及其影响因素。实证结果显示:中国居民收入分布变迁的速度与经济体制改革进程相对应;经济增长因素是引起居民收入分布变迁的主要因素,在提高总体居民收入水平的同时加剧了居民收入分布的极化程度;收入分配因素对居民收入分布变迁的作用相对较弱,但有一定的减贫或缩小居民收入差距作用。     

A robust test for asymptotic independence of bivariate extremes

We show that the existing tests for asymptotic independence are sensitive to outliers. A robust test is proposed. The new test is made stable under contamination through a shrinkage scheme. Simulations show that the new test performs well in the presence of contaminated data while maintaining good properties when there is no contamination. An application to real data shows the added value of our new robust approach.     

Statistical inference on asymptotic properties of two estimators for the partially linear single-index models

The outer product of gradients (OPG) estimation procedure based on least squares (LS) approach has been presented by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] to estimate the single-index parameter in partially linear single-index models (PLSIM). However, its asymptotic property has not been established yet and the efficiency of LS-based method can be significantly affected by outliers and heavy-tailed distributions. In this paper, we firstly derive the asymptotic property of OPG estimator developed by Xia et al. [An adaptive estimation of dimension reduction space. J Roy Statist Soc Ser B. 2002;64:363–410] in theory, and a novel robust estimation procedure combining the ideas of OPG and local rank (LR) inference is further developed for PLSIM along with its theoretical property. Then, we theoretically derive the asymptotic relative efficiency (ARE) of the proposed LR-based procedure with respect to LS-based method, which is shown to possess an expression that is closely related to that of the signed-rank Wilcoxon test in comparison with the t-test. Moreover, we demonstrate that the new proposed estimator has a great efficiency gain across a wide spectrum of non-normal error distributions and almost not lose any efficiency for the normal error. Even in the worst case scenarios, the ARE owns a lower bound equalling to 0.864 for estimating the single-index parameter and a lower bound being 0.8896 for estimating the nonparametric function respectively, versus the LS-based estimators. Finally, some Monte Carlo simulations and a real data analysis are conducted to illustrate the finite sample performance of the estimators.     

An algorithm for the minimum sum of weighted absolute errors regression

We propose an algorithm to estimate the unknown constants in a multiple linear regression model under the minimum sum of weighted absolute errors (MSWAE). The proposed algorithm, a generalization of an earlier algorithm, is compared to a bounded variable algorithm. Some somputational experience is reported.