Abstract: B-optimal robust estimates are considered for semiparametric exponential mixture models, under the perception that the data may have been contaminated. The B-optimal robust influence functions are defined by Hampel's variational problem: minimizing the asymptotic variances over the class of influence functions bounded by a constant. Explicit B-optimal influence functions are calculated for the semiparametric exponential mixture models. The one-step procedure is used to construct the B-optimal robust estimates from the B-optimal influence functions. A small Monte-Carlo study is conducted for the semiparametric two-sample exponential mixture model to confirm the theory.
Key words and phrases: B-optimal, bounded influence function, exponential mixture model, Hampel's problem, most robust estimate.