  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.
