Nonparametric modal regression with missing response observations

Modal regression has emerged as a flexible alternative to classical regression models when the conditional mean or median are unable to adequately capture the underlying relation between a response and a predictor variable. This approach is particularly useful when the conditional distribution of the response given the covariate presents several modes, so the suitable regression function is a multifunction. In recent years, some proposals have addressed modal (smooth) regression estimation using kernel methods. In addition, some remarkable extensions to deal with censored, dependent or circular data have been also introduced. However, the case of incomplete samples due to missingness has not been studied in the literature. This paper adapts the nonparametric modal regression tools to handle missing observations in the response, investigating several imputation approaches through an extensive simulation study. The performance in practice of our proposals are also illustrated with two real--data examples.