Combining regression mean and quantile estimators

In the presence of multiple candidate regression procedures, focus has been put on either selecting the "best" or combining them globally. For a selection strategy, however, the local strengths (if strong) of the competing candidate(s) of the global "winner" should be realized. This issue also exists for global model combination methods such as Bayesian Model Averaging (see, for example, Hoeting et al., 1999) and Adaptive Regression by Mixing (Yang, 2001). We design a diagnostic measure to assess the local performance of global selection. We then propose a general methodology of local selection/combination to take into account such local performance variation. Theoretical and numerical results demonstrate the usefulness of our local methods.; Another topic we worked on is in the context of conditional quantile estimation, which is very useful in areas such as economics and finance. Differently from mean regression problems, quantile estimation at various probability levels gives us a more complete picture of the conditional distribution of a response Y given input X = x. Motivated by the success of model combination methods for mean regression problems, we present a model combination algorithm for quantile estimation. Some theoretical results as well as numerical output are provided to illustrate the advantage of our proposed method.