A Correction to 'Generalized Nonparametric Smoothing With Mixed Discrete and Continuous Data' by Li, Simar & Zelenyuk

Li & Racine (2004) have proposed a nonparametric kernel-based method for smoothing in the presence of categorical predictors as an alternative to the classical nonparametric approach that splits the data into subsets (‘cells’) defined by the unique combinations of the categorical predictors. Li, Simar & Zelenyuk (2014) present an alternative to Li & Racine’s (2004) method that they claim possesses lower mean square error and generalizes and improves upon the existing approaches. However, these claims do not appear to withstand scrutiny. A number of points need to be brought to the attention of practitioners, and two in particular stand out; a) Li et al.’s (2014) own simulation results reveal that their estimator performs worse than the existing classical ‘split’ estimator and appears to be inadmissible, and b) the claim that Li et al.’s (2014) estimator dominates that of Li & Racine (2004) on mean square error grounds does not appear to be the case. The classical split estimator and that of Li & Racine (2004) are both consistent, and it will be seen that Li & Racine’s (2004) estimator remains the best all around performer. And, as a practical matter, Li et al.’s (2014) estimator is not a feasible alternative in typical settings involving multinomial and multiple categorical predictors.