Adaptive kernel conditional density estimation

Abstract A methodology is proposed for the determination of factor-dependent bandwidths for the kernel-based estimation of the conditional density $\rho (x|z)$ underlying a set of observations. The adaptive determination of the bandwidths is based on a $z$-dependent effective number of samples and variance. The procedure extends to categorical factors, where a non-trivial ‘bandwidth’ can be designed that optimally uses across-class information while capturing class-specific traits. A hierarchy of algorithms is developed, and their effectiveness is demonstrated on synthetic and real-world data.