Central Limit Theorem for Asymmetric Kernel Functionals.

Asymmetric kernels are quite useful for the estimation of density functions which have bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. This paper extends the central limit theorem for degenerate U-statistics in order to compute the limiting distribution of certain asymmetric kernel functionals.