We establish a general uniform in bandwidth consistency result for kernel estimators of the unconditional and conditional joint density of a distribution, which is defined by a mixed discrete and continuous random variable.
"Uniform in bandwidth consistency of kernel estimators of the density of mixed data." Electron. J. Statist. 9 (1) 1518 - 1539, 2015. https://doi.org/10.1214/15-EJS1049