On some classifiers based on multivariate ranks

Non parametric approaches to classification have gained significant attention in the last two decades. In this paper, we propose a classification methodology based on the multivariate rank functions and show that it is a Bayes rule for spherically symmetric distributions with a location shift. We show that a rank-based classifier is equivalent to optimal Bayes rule under suitable conditions. We also present an affine invariant version of the classifier. To accommodate different covariance structures, we construct a classifier based on the central rank region. Asymptotic properties of these classification methods are studied. We illustrate the performance of our proposed methods in comparison to some other depth-based classifiers using simulated and real data sets.     

Basic concepts of multiple tests — A survey

It is the purpose of this paper to review the main aspects related to multiple test problems. This concerns among others the particularities of multiple tests as for instance the formulation of restrictions to avoid inconsistent decisions and of criteria to control for a multiple type I error rate. In addition, the basic principles for constructing multiple tests are introduced and their properties are summarized. The paper closes with giving a rough idea of further special multiple test problems and their corresponding test procedures.     

死刑赦免:限制死刑的一种新选择

死刑赦免制度,是指核准死刑的判决、裁定生效后,如果该罪犯确有悔改或者立功表现,或者具有法律规定的其他特定条件,应当停止死刑命令的执行,并且依法定程序报告最高人民法院,由最高人民法院发布死刑赦免令,赦免其死刑而改判其他刑罚的制度。这一制度的建立,可以消除我国刑事诉讼程序中的若干矛盾,也有利于进一步贯彻"少杀、慎杀"的死刑政策,有利于避免错杀,同时也能够更好地履行我国的国际义务。     

控制犯罪与保障人权双重视野下的侦查程序的改革与完善——以公安机关的侦查活动为视角

控制犯罪与保障人权,是现代刑事司法活动的基本价值取向。现行《刑事诉讼法》及修正后的《刑事诉讼法》在控制犯罪和保障人权的价值平衡方面存在不足,主要表现在：程序设计上权力运行的失衡;错误拘留国家赔偿制度的掣肘;部分特殊立法缺失;立案、拘留、逮捕、讯问、搜查和扣押措施执行不规范。其主要原因是：立法层面——立法理念有失偏颇;体制层面——侦查权力配置上的错位;机制方面——警力配置及警察权利保护不足。应从修改完善《刑事诉讼法》、增加特别立法以及制定完善公安机关部门规章、规定三个方面入手。     

Sensitive parameters

Notions such as robustness and resistance of an estimator are well known and useful. These ideas have not been fully extended to functional parameters, although it seems natural to do so. In this paper we define a sensitive parameter as one for which small changes in the underlying distribution cause large changes in the parameter value. It is demonstrated that no nontrivial, nonparametric confidence procedure can exist for such a parameter. This extends a result of Bahadur and Savage ( 1956 ). The relationship between this definition and some standard concepts in robustness theory are explored, and implications for parametric inference are studied.     

Bayes two-decision procedures for two-sample problems and rank-order data

A two-sample problem for rank-order data is formulated as a two-decision problem. Using the general Bayes solution, Bayes procedures are derived for several configurations of the set of states of nature including some for which the problem is distribution-free. It is shown that for certain prior distributions these procedures reduce to classical LMP rank tests. Some devices for selection of prior distributions are suggested. It is shown that the Bayes risk of these procedures tends to zero as sample sizes increase.     

Residual components in generalized linear models

The adequacy of a postulated generalized linear model can often be improved by transforming predictors and/or including additional explanatory variables. To assess the fit relative to a given predictor, we define its corresponding residual component. Asymptotic bias and variance of the residual component are considered, paying particular attention to the case that the presumed model is valid.     

Multiple Comparisons Controlling Expected Number of False Discoveries

In this paper, it is put forward that the task of designing a procedure for a set of multiple comparisons should be considered as a decision-making under uncertainty. Due to this motivation, for the problem of multiple comparisons, we considered another error rate to be controlled, called PFER (per-family error rate), which requests that the expected number of false rejections of a test procedure should be bounded no more than a prespecified level k. Although PFER was proposed by Tukey in 1953, there is not much studying about it so far. We first present Bonferroni procedure (single-step) and then build two step-up procedures with one having generic critical values and another using critical values in BH (Benjamini and Hochberg) type. These procedures are compared through simulations.