The BACON-EEM algorithm for multivariate outlier detection in incomplete survey data

With complete multivariate data the BACON algorithm (Billor, Hadi and Vellemann 2000) yields a robust estimate of the covariance matrix. The corresponding Mahalanobis distance may be used for multivariate outlier detection. When items are missing the EM algorithm is a convenient way to estimate the covariance matrix at each iteration step of the BACON algorithm. In finite population sampling the EM algorithm must be enhanced to estimate the covariance matrix of the population rather than of the sample. A version of the EM algorithm for survey data following a multivariate normal model, the EEM algorithm (Estimated Expectation Maximization), is proposed. The combination of the two algorithms, the BACON-EEM algorithm, is applied to two datasets and compared with alternative methods.