Cross-validation is the most common data-driven procedure for choosing smoothing parameters in nonparametric regression. For the case of kernel estimators with iid or strong mixing data, it is well-known that the bandwidth chosen by cross-validation is optimal with respect to the average squared...

This paper provides distribution free tests for detecting sample selection in conditional quantile functions. The first test is an omitted predictor test with the propensity score as the omitted variable. In the case of rejection we cannot distinguish between rejection due to genuine selection...