  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.
