Model Averaging based Semiparametric Modelling for Conditional Quantile Prediction

In real data analysis, the underlying model is usually unknown, modelling strategy plays a key role in the success of data analysis. Stimulated by the idea of model averaging, we propose a novel semiparametric modelling strategy for conditional quantile prediction, without assuming the underlying model is any specific parametric or semiparametric model. Thanks the optimality of the selected weights by cross-validation, the proposed modelling strategy results in a more accurate prediction than that based on some commonly used semiparametric models, such as the varying coefficient models and additive models. Asymptotic properties are established of the proposed modelling strategy together with its estimation procedure. Intensive simulation studies are conducted to demonstrate how well the proposed method works, compared with its alternatives under various circumstances. The results show the proposed method indeed leads to more accurate predictions than its alternatives. Finally, the proposed modelling strategy together with its prediction procedure are applied to the Boston housing data, which result in more accurate predictions of the quantiles of the house prices than that based on some commonly used alternative methods, therefore, present us a more accurate picture of the housing market in Boston.