Nonparametric regression with discrete covariate and missing values

We consider nonparametric regression with a mixture of continuous and discrete explanatory variables where realizations of the response variable may be missing. An imputation based nonparametric regression estimator is proposed. We show that the proposed approach leads to a leading order variance benefit, whereas smoothing the categorical variables gives a second order variance improvement. We also demonstrate the applications of the proposed approach through numerical simulations and two practical examples.