University of Oxford Department of Satistics Graduate Student
Covariance and correlation estimates have many important applications. In the presence of outliers, maximum likelihood estimates of covariance and correlation matrices are not reliable. A small fraction of outliers, in some cases even a single outlier, can distort the maximum likelihood covariance and correlation estimates making them virtually useless. That is, correlations for the vast majority of the data can be erroneously reported and multidimensional outlier detection can fail to detect outliers. My talk will cover the Orthogonalized Gnanadesikan-Kettenring (OGK) covariance estimator. The OGK provides a robust estimate; that is it provides a reliable estimate of the covariance matrix for the bulk of the data when there are a small fraction of outliers in the data. The OKG estimator uses an intuitive approach followed by a clever correction to insure that the covariance matrix estimate is positive definite.