Estimation of Contamination Parameters and Identification of Outliers in Multivariate Data

Abstract

Multivariate outliers may be modeled using the contaminated multivariate normal distribution with two parameters indicating the percentage of outliers and the degree of contamination. Recent developments in elliptical distribution theory are used to determine estimators of these parameters. These estimators can be used with an index of Mahalanobis distance to identify the multivariate outliers, which can then be eliminated to obtain approximately normal data. The performance of the proposed estimators and outliers rejection procedures are evaluated in a small simulation study.

Robust Mean and Covariance Structure Analysis Through Iteratively Reweighted Least Squares

“…Methods for outlier detection followed by a classical method have been proposed in covariance structure literature (Berkane & Bentler, 1988;Bollen, 1987;Cadigan, 1995;Lee & Wang, 1996;Tanaka et al, 1991). Since the most influential points may not be outliers if the data set is from a distribution with heavy tails, after the most influential points are identified, a decision has to be made on whether to remove the "outliers" in further analysis.…”

Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers

“…Thus, once the observation has been classified in one of the K states, the approach reveals richer information about the role of that observation in that state. Note also that, the resulting information can be used to possibly eliminate the outliers if such an outcome is desired (Berkane and Bentler, 1988); in such a case, the remaining data may then be treated as effectively being distributed according to a N-HMRM, and the clustering results can be reported as usual.…”

Outlier Impact and Accommodation Methods: Multiple Comparisons of Type I Error Rates

“…Thus, for a normally distributed data set, the common rule is that an outlier is any value that is beyond ± 3 standard deviations from the mean. In addition, for different research designs and methods of analysis, there are different approaches developed to detect outliers (Barnett & Lewis, 1994;Berkane & Bentler, 1988;Cook, 1986;Gnanadesikan, 1997;Jarrell, 1991). Some approaches are adapted from univariate methods, such as frequency tables, histograms, and box plots (Allison, Gorman, & Primaverya, 1993;Jarrell, 1991); some use residuals of various kinds (Cook, 1986;David, 1978); others suggest bivariate and multivariate techniques such as Cook's distance (Allison et al, 1993), principal components (Hawkins, 1974), hat matrix (Hoaglin & Welsch, 1978), and Mahalanobis distance (Stevens, 1984).…”