Resistant orthogonal procrustes analysis

In this paper two alternative loss criteria for the least squares Procrustes problem are studied. These alternative criteria are based on the Huber function and on the more radical biweight function, which are designed to be resistant to outliers. Using iterative majorization it is shown how a convergent reweighted least squares algorithm can be developed. In asimulation study it turns out that the proposed methods perform well over a specific range of contamination. When a uniform dilation factor is included, mixed results are obtained. The methods also yield a set of weights that can be used for diagnostic purposes.     

基于异常值检验的Bayesian方法验前信息可信度计算

由于采用了验前信息,Bayesian方法为小子样条件下的装备试验与评价提供了可行的理论依据,从而在装备试验与评价领域得到了广泛的应用。然而,由于验前信息具有多源性及主观性,当采用其进行Bayesian统计推断时,可能会导致Bayesian统计推断的结果偏差较大,使得决策风险增加。因此,研究Bayesian方法中验前信息的可信度显得至关重要。在现场试验样本信息已知的前提下,给出了验前信息可信度的定义,提出一种基于异常值检验的验前信息可信度计算方法,并基于Matlab数学软件,通过仿真思路实现了算法求解。最后,以某雷达探测距离试验为例,证明方法具有科学合理性。     

Robust classification procedures based on dichotomous and continuous variables

For classifying a univariate or a multivariate observation in one of the two populations, Tiku and Balakrishnan (1984) and Balakrishnan, Tiku and Shaarawi (1985) developed robust (to departures from normality) procedures. These procedures are extended here to situations where the classification has to be based on the observed value of a pair of variables, one being a dichotomous random variable and the other a univariate or a multivariate continuous random variable.We are very grateful to the referees for their comments which led to a substantial improvement of an earlier draft of this paper. Thanks are also due to the Natural Sciences and Engineering Council of Canada for a research grant to M.L. Tiku.     

多元正态样本中Outliers的不一致性检验

多元数据中的Outliers的不一致性检验与一元数据的Outliers的不一致性检验同样重要,而且是相关联的.本文讨论了m元正态样本的n个个体的马氏距离的极端值,并给出检验这些极端值不一致性的方法.     

Robust exponential smoothing

The paper is devoted to robust modifications of exponential smoothing for time series with outliers or long-tailed distributions. Classical exponential smoothing applied to such time series is sensitive to the presence of outliers or long-tailed distributions and may give inadequate smoothing and forecasting results. First, simple and double exponential smoothing in the L₁ norm (i.e. based on the least absolute deviations) are discussed in detail. Then, general exponential smoothing is made robust, replacing the least squares approach by M-estimation in such a way that the recursive character of the final formulas is preserved. The paper gives simple algorithmic procedures which preserve advantageous features of classical exponential smoothing and, in addition, which are less sensitive to outliers. Robust versions are compared numerically with classical ones.     

TESTING FOR OUTLIERS IN TIME SERIES USING WAVELETS

One remarkable feature ofwavelet decomposition is that the wavelet coefficients are localized, and any singularity in the input signals can only affect the wavelet coefficients at the point near the singularity. The localized property of the wavelet coefficients allows us to identify the singularities in the input signals by studying the wavelet coefficients at different resolution levels. This paper considers wavelet-based approaches for the detection of outliers in time series. Outliers are high-frequency phenomena which are associated with the wavelet coefficients with large absolute values at different resolution levels. On the basis of the first-level wavelet coefficients, this paper presents a diagnostic to identify outliers in a time series. Under the null hypothesis that there is no outlier, the proposed diagnostic is distributed as a X1^2. Empirical examples are presented to demonstrate the application of the proposed diagnostic.     

基于纵横距离的单纯异常点检测算法及应用

首先讨论了异常点挖掘在数据挖掘过程中的重要性,产生异常点的原因,以及目前用于检测异常点的常用算法,指出了单纯应用距离法的局限性,提出了基于纵横距离的异常点检测算法,并给出了基于学生成绩检测的应用实例,该方法不需要进行大量的样本训练,在异常点检测方面有较好的效果.     

Robust Double Clustering: A Method Based on Alternating Concentration Steps

We propose two algorithms for robust two-mode partitioning of a data matrix in the presence of outliers. First we extend the robust k-means procedure to the case of biclustering, then we slightly relax the definition of outlier and propose a more flexible and parsimonious strategy, which anyway is inherently less robust. We discuss the breakdown properties of the algorithms, and illustrate the methods with simulations and three real examples. The author is grateful to four referees for detailed suggestions that led to an improved paper, and to Professor Vichi for support and careful reading of a first draft. Acknowledgements go also to Francesca Martella for advice.     

A comparison of forecasts from least absolute value and least squares regression

A Monte Carlo simulation is used to compare forecasts from least absolute value and least squares estimated regression equations. When outliers are present, the least absolute value forecasts are shown to be superior to least squares forecasts. The results emphasize the importance of exercising caution when using forecasts from least squares estimated regressions. Use of least absolute value regression (or some other robust regression method) instead of, or as an adjunct to, least squares is recommended. The comparison of forecasts from the two methods provides one way of assessing whether the least squares forecasts have been adversely affected by outliers. If outliers are present, the least absolute value regression forecasts can be used.