Semiparametric model averaging for high dimensional conditional quantile prediction

TL;DR

This paper introduces a robust semiparametric model averaging method for high-dimensional conditional quantile prediction, combining local linear regression and penalized estimation to select significant variables.

Contribution

It proposes a novel two-step estimation procedure that effectively estimates and combines marginal quantile functions in high-dimensional settings.

Findings

The method accurately predicts conditional quantiles in simulations.

It effectively selects significant variables for quantile estimation.

Asymptotic properties of the estimator are established.

Abstract

In this article, we propose a penalized high dimensional semiparametric model average quantile prediction approach that is robust for forecasting the conditional quantile of the response. We consider a two-step estimation procedure. In the first step, we use a local linear regression approach to estimate the individual marginal quantile functions, and approximate the conditional quantile of the response by an affine combination of one-dimensional marginal quantile regression functions. In the second step, based on the nonparametric kernel estimates of the marginal quantile regression functions, we utilize a penalized method to estimate the suitable model weights vector involved in the approximation. The objective of the second step is to select significant variables whose marginal quantile functions make a significant contribution to estimating the joint multivariate conditional quantile function. Under some mild conditions, we have established the asymptotic properties of the proposed robust estimator. Finally, simulations and a real data analysis have been used to illustrate the proposed method.