Abstract: This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of models via tensor product splines is demonstrated through examples. The computation of estimates with automatic multiple smoothing parameters is also discussed. Data examples are presented to illustrate possible applications of the technique. For theoretical justification of the method, an asymptotic theory is sketched in the appendix.
Key words and phrases: ANOVA decomposition, conditional distribution, density estimation, penalized likelihood, rate of convergence, regression, smoothing parameter.