An Extension of the Normal/Independent Family for Studies of Robust Estimators

The family of normal scale mixture distributions, also called the Normal/Independent family, has been used for efficient Monte Carlo studies of robust estimators. The distributions in this family are unimodal. The Normal/Independent family is extended by introducing a location mixing in addition to the scale mixing. Distributions in this extension may be nonunimodal. The asymptotic variances of robust estimators of location are compared using the distributions from the extension. A Monte Carlo swindle similar to the one used in the Princeton study is given for the extended family. A small simulation study demonstrates the efficiency of the swindle. The swindle is compared with other swindle methods based on Fisher's score function and regression.