Nonparametric Estimation of Conditional Distributions in the Presence of Continuous and Categorical Data

A method is proposed for the consistent nonparametric estimation of conditional probability and probability density functions along with associated gradients when both the conditioned and conditioning variables are categorical, continuous, or a mixture of both types. The method builds on the work of Aitchison & Aitken (1976) who proposed a novel method for kernel density estimation when using multinomial categorical data types. Simulations show that the proposed method performs quite well for a number of conditional simulated processes that mix both categorical and continuous variables. Applications of the proposed method to (i) the widely-cited Iris dataset of Fisher (1936), (ii) the female labor supply dataset from the Panel Study on Income Dynamics examined in Mroz (1987), and (iii) the Swiss labor force data studied by Gerfin (1996) all demonstrate that the proposed method performs better than conventional parametric models for predicting multinomial discrete choice. The method extends the realm of nonparametric modeling through the seamless blending of both categorical and continuous variables, and is capable of detecting structure in the data which frequently remains undetected by conventional parametric approaches.