Jackknife Partially Linear Model Averaging for the Conditional Quantile Prediction

TL;DR

This paper introduces a semiparametric model averaging approach for conditional quantile prediction that remains robust under model misspecification, optimizing out-of-sample accuracy through cross-validation.

Contribution

It develops a novel model averaging method for conditional quantile estimation using partially linear models with data-driven weight selection, ensuring asymptotic optimality.

Findings

The proposed method outperforms traditional approaches in simulations.

It achieves asymptotic optimality in quantile prediction error.

Application demonstrates superior predictive accuracy over existing methods.

Abstract

Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric model averaging to predict the conditional quantile even if all models under consideration are potentially misspecified. Specifically, we first build a series of non-nested partially linear sub-models, each with different nonlinear component. Then a leave-one-out cross-validation criterion is applied to choose the model weights. Under some regularity conditions, we have proved that the resulting model averaging estimator is asymptotically optimal in terms of minimizing the out-of-sample average quantile prediction error. Our modelling strategy not only effectively avoids the problem of specifying which a covariate should be nonlinear when one fits a partially linear model, but also results in a more accurate prediction than traditional model-based procedures because of the optimality of the selected weights by the cross-validation criterion. Simulation experiments and an illustrative application show that our proposed model averaging method is superior to other commonly used alternatives.