Information and Posterior Probability Criteria for Model Selection in Local Likelihood Estimation

Local likelihood estimation has proven to be an eeective method for obtaining estimates of parameters that vary with a covariate. To obtain useful estimates of such parameters, approximating models are used. In such cases it is useful to consider window based estimates. We may need to choose between competing approximating models. In this paper we propose a modiication to the methods used to motivate many information and posterior probability criteria for the weighted likelihood case. We derive weighted versions for two of the most widely known criteria, namely the AIC and BIC. Via a simple modiication, the criteria are also made useful for window span selection. The usefulness of the weighted version of these criteria are demonstrated through a simulation study and an application to three data sets.