Outlier detection for high dimensional data using the Comedian approach

The process of detection of outliers is an interesting and important aspect in the analysis of data, as it could impact the inference. There are various methods available in the literature for detection of outliers in multivariate data [V. Barnett and T. Lewis, Outliers in Statistical Data, John Wiley & Sons, Chichester, 1994] using the Mahalanobis distance measure. An attempt is made to propose an alternate method of outlier detection based on the comedian introduced by Falk [On MAD and Comedians, Ann. Inst. Statist. Math. 49 (1997), pp. 615–644]. The proposed method is computationally efficient with high breakdown value and low computation time. Further, important properties, namely, success rates (SR) and false detection rates (FDR) are studied and compared with some of the well-known outlier detection methods through a simulation study. The Comedian method has high SR and low FDR for all combination of parameters. On removal of the detected outliers or down weighing, the same, highly robust and approximately affine equivariant estimators of multivariate location and scatter can be obtained. Finally, the method is applied to well-known real data sets to evaluate its performance.     

On the choice of the prior distribution in hypergeometric sampling

Information in a statistical procedure arising from sources other than sampling is called prior information, and its incorporation into the procedure forms the basis of the Bayesian approach to statistics. Under hypergeometric sampling, methodology is developed which quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information embedded in any prior distribution. The most conservative prior distribution from a specified class (each member of which carries the available prior information) is that prior distribution within the class over which the likelihood function has the greatest average domination. Four different families of prior distributions are developed by considering a Bayesian approach to the formation of lots. The most conservative prior distribution from each of the four families of prior distributions is determined and compared for the situation when no prior information is available. The results of the comparison advocate the use of the Polya (beta-binomial) prior distribution in hypergeometric sampling.     

相位无线电导航系统主、副台的合理布设及其定位误差分析

本文论述了相位无线电导航系统主、副台台址的选择与作用距离,覆盖区大小及其定位误差的关系,介绍了为实现最佳定位而正确选择台址的经验和计算曲线,并指出实际架台时应注意的若干问题。     

On minimum Hellinger distance estimation

Efficiency and robustness are two fundamental concepts in parametric estimation problems. It was long thought that there was an inherent contradiction between the aims of achieving robustness and efficiency; that is, a robust estimator could not be efficient and vice versa. It is now known that the minimum Hellinger distance approached introduced by Beran [R. Beran, Annals of Statistics 1977;5:445–463] is one way of reconciling the conflicting concepts of efficiency and robustness. For parametric models, it has been shown that minimum Hellinger estimators achieve efficiency at the model density and simultaneously have excellent robustness properties. In this article, we examine the application of this approach in two semiparametric models. In particular, we consider a two‐component mixture model and a two‐sample semiparametric model. In each case, we investigate minimum Hellinger distance estimators of finite‐dimensional Euclidean parameters of particular interest and study their basic asymptotic properties. Small sample properties of the proposed estimators are examined using a Monte Carlo study. The results can be extended to semiparametric models of general form as well. The Canadian Journal of Statistics 37: 514–533; 2009 © 2009 Statistical Society of Canada     

距离与活力——再思文化的多元性

文化以复数的形式存在,不同的文化在进行一致化的同时也在持续地特征化和个体化。从差异的角度思考文化的多元性,将会使文化归属变成一种认同论述;而从距离的角度来审视文化的多元性,将会展现出一切富有创意的可能性的开放。事实上,文化距离是可开发的资源。对于广受关注的人权问题,可以对人权的普遍性达成共识的是:人权所否定的东西比肯定的东西更有普遍性。面对文化冲突,是理解而非妥协才是解决之道。在文化对话(dia-logue)里,距离(dia-)使分开的事物之间维持着互动关系,而所有的文化都互相保持着一种原则可通性,并且属于文化的一切都是可以理解的。不同文化之间每一方都应该开放其立场,用各自的语言,共同在有距离的立场之间寻找理解对方。这也要求每一方再次审视自己的理念,从而进入与另一方的沟通。     

艺术的“画框”效应界定艺术的一种尝试

界定艺术一直是艺术理论上的难题,面对实践与理论上更加严峻的挑战,一些理论家转而寻求通过艺术与非艺术之间的界线来界定艺术。在这界线中产生的“画框效应”源于艺术的本性,包涵艺术的两大功能性特征：距离与突显。将它作为界定艺术的一种标准,即通过艺术的功能来认定艺术,虽然存在一定困难,却不失为一种有益的尝试。     

The social distance of Poles to other minorities: a study of four cities in Germany and Britain

This contribution investigates the social distance of immigrants from Poland in four Western European cities – London, Birmingham, Berlin and Munich – particularly Polish immigrants’ distance towards members of ethnic, religious and sexual minorities in their various social roles. Presenting unique data from the first wave of a longitudinal qualitative study, we first discuss the differential levels of social distance that Polish immigrants place between themselves and members of minority groups in each city. We find that respondents’ socio-demographic characteristics impact their social distance, but their education and occupation may have less of an effect than their place of origin in Poland or current place of residence and work. Moreover, these factors work differentially across the four cities. After analysing social distance with respect to three dimensions of difference – ethnicity, religion and sexuality – we find several different social-distancing mechanisms. Ultimately, we argue that social science needs to consider regional and local contexts in which social attitudes towards minorities are acquired and exercised. Similarly, we need to reflect on the group’s presumed homogeneity and on the unifying visions of the ‘host society’ as a site of migrants’ incorporation.     

Bayes prediction of Poisson regression superpopulation mean with a non gamma prior

We consider Khamis' (1960) Laguerre expansion with gamma weight function as a class of “near-gamma” priors (K-prior) to obtain the Bayes predictor of a finite population mean under the Poisson regression superpopulation model using Zellner's balanced loss function (BLF). Kullback–Leibler (K-L) distance between gamma and some K-priors is tabulated to examine the quantitative prior robustness. Some numerical investigations are also conducted to illustrate the effects of a change in skewness and/or kurtosis on the Bayes predictor and the corresponding minimal Bayes predictive expected loss (MBPEL). Loss robustness with respect to the class of BLFs is also examined in terms of relative savings loss (RSL).     

面板数据加权聚类分析方法研究

在面板数据聚类分析方法的研究中,基于面板数据兼具截面维度和时间维度的特征,对欧氏距离函数进行了改进,在聚类过程中考虑指标权重与时间权重,提出了适用于面板数据聚类分析的"加权距离函数"以及相应的Ward.D聚类方法。首先定义了考虑指标绝对值、邻近时点增长率以及波动变异程度的欧氏距离函数;然后,将指标权重与时间权重通过线性模型集结成综合加权距离,最终实现面板数据的加权聚类过程。实证分析结果显示,考虑指标权重与时间权重的面板数据加权聚类分析方法具有更好的分辨能力,能提高样本聚类的准确性。     

On compounded geometric distributions and their applications

Here, we introduce two-parameter compounded geometric distributions with monotone failure rates. These distributions are derived by compounding geometric distribution and zero-truncated Poisson distribution. Some statistical and reliability properties of the distributions are investigated. Parameters of the proposed distributions are estimated by the maximum likelihood method as well as through the minimum distance method of estimation. Performance of the estimates by both the methods of estimation is compared based on Monte Carlo simulations. An illustration with Air Crash casualties demonstrates that the distributions can be considered as a suitable model under several real situations.