Weighted Likelihood Estimation
We propose to use weighted likelihood to combine information from related populations to yield a better estimator than the classical MLE. We will show that the proposed weighted likelihood function can be derived from an information theoretic framework. We propose to choose the likelihood weights adaptively by using cross-validation. The asymptotic properties of the weighted likelihood estimator (WLE) will be presented. The connection between the weighted likelihood and hierachical Bayesian approach will also be discussed.