Sequential Application of Multivariate Outlier Test : a Robust Approach

Identification of outliers in multivariate data is not trivial. especially when there exists several outliers in the data. The classical identification method based on the sample mean and sample covariance matrix cannot always find them, because the classicd rnean and covariance matris are themselves affected by outliers. This problem is termed as masting7 because the outliers get maslied by each other. To avoid the masking effect. robust estimates of mean and covariance are siiggested by many aut hors. This thesis deals with the problem of identifying and testing a set of a number k of extreme sample points as significant outliers in a sample of size n drawn from a pdimensional normal distri bution wit h unknown parameters. A robust sequential proccdurc is suggcstcd for thc idcntification of multipleoutliers in multivariate normal data. Chapter 1 gives a brief idea about outliers in statisticai data. In Chapter 2 %e review the rejection techniques for single and multiple outliers suggested by different authors. GVe also review some recent papers which deal with the problem of accommodation and identification of multiple outliers using robust procedures. In Chapter 3 we propose a test criterion for the detection of multivariate outliers based on the robust estimates of rnean and covariance. Chapter 4 deals with the application of our proposed test procedure with different examples. A simulation study is carried out to support the good behaviour of the proposed sequential test when the data are multivariate normal. We also study the performance of the proposed sequential test in the presence of outliers.