A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions

Nonparametric conditional density functions are widely used in applied econometric and statistical modelling because they provide enriched information summaries of the relationships between dependent and independent variables. Although least-squares cross-validation is considered to be the best criterion for bandwidth selection of the kernel estimator of the conditional density, the number of computations required for this procedure grows exponentially as the number of observations increases. A fast algorithm is proposed to reduce this computational cost, and its accuracy and efficiency are verified via numerical experiments. A practical application is also presented to demonstrate the algorithm's potential usefulness.