Outlier detection for high dimensional data using the Comedian approach

Multivariate outlier detection based on a robust Mahalanobis distance with shrinkage estimators

“…A simulation study is performed considering a p−dimensional random variable X following a contaminated multivariate normal distribution given as a mixture of normals of the form (1 − α)N (0, I) + αN (δe, λI), where e denotes the p−dimensional vector of ones. This model is analogous to the one used by Rousseeuw and Driessen [1999], Peña and Prieto [2001], Filzmoser et al [2005], Peña and Prieto [2007], Maronna and Zamar [2002] and Sajesh and Srinivasan [2012]. This experiment has been conducted for different values of the samplespace dimension p = 5, 10, 30, and the chosen sample size in relation to the dimension was n = 100, 100, 500, respectively.…”

“…For the methods mentioned in previous sections some measures are studied: the correct detection rates (c) and the false detection rates (f). The method MCD refers to the RMD based on the MCD estimator and with the classical threshold, the method Adj MCD refers to the latter distance considering the adjusted quantile of Filzmoser et al [2005], the method Kurtosis refers to the Peña and Prieto [2007] approach, the method OGK refers to the Orthogonalized Gnanadesikan-Kettenring method proposed by Maronna and Zamar [2002] and COM is the Comedian method proposed by Sajesh and Srinivasan [2012]. We have also presented the results for the collection RMDv1 -RMDv6 proposed in Table 1.…”

“…Maronna and Zamar [2002] and Sajesh and Srinivasan [2012] proposed to investigate the lack of equivariance with transformed data, by simulations. We study the same for our proposal.…”

“…Thus, it is necessary to use the correct and false detection rates for studying the breakdown value of the outlier detection procedure. Analogously as Sajesh and Srinivasan [2012], we consider two forms of contamination: α percent symmetric, for which the ith observation is multiplied by 100i, and α percent asymmetric, for which the ith observation is replaced by (100i)e, i = 1, ..., nα, where e = (1, ..., 1). In the first case the outliers are symmetrically distributed, and asymmetrically in the second case.…”

An Overview of Multiple Outliers in Multidimensional Data

“…Sajesh and Srinivasan [63] proposed a method for the detection of outliers in multivariate data based on comedian, an alternative measure of dependence between two random variables introduced by Falk [64]. Let X and Y be two random variables then the comedian of X and Y is defined as…”