On additive conditional quatiles with high-dimensional covariates

We investigate the estimation of the conditional quantile when many covariates are involved. In particular, we model the conditional quantile of a response as a nonlinear additive function of relevant covariates. For this setup, we propose a nonparametric smoother to estimate the unknown functions. The estimator provides direct computation of the nonlinear functions. Because it does not require any iteration, the estimator allows fast and routine data analysis. On the theoretical front, we also show asymptotic properties of the estimator, including mean squared error and limiting distribution. The theory confirms that for moderate dimension of the covariates, the estimator escapes the "curse of dimensionality" problem. Both simulated and real data examples are provided to illustrate the methodology.