Nonparametric Adaptive Likelihood Weights.

Abstract. The weighted likelihood can be used to make inference about one pop-ulation when data from m − 1 similar populations are also available. We show how this method can be seen as a special case of the Entropy Maximization Prin-ciple. A heuristic development leads to a new proposal for data-based weights that we call MAMSE (Minimum Averaged Mean Squared Error) weights. We present an algorithm for calculating the weights and use the Kuhn-Tucker suf-ficient conditions to show that it yields the appropriate minimum. The perfor-mance and properties of the weighted likelihood based on MAMSE weights are then explored through simulations.