Multivariate Boundary Kernels from Local Linear Estimation

Lejeune and Sarda (1992) and Jones (1993) introduced the principle of local linear estimation to nonparametric estimation of smooth densities on the positive real axes. This methodology results in the basic kernel smoother with Gasser and Müller (1979) type boundary kernels when estimating close to a boundary. This principle is extended to nonparametric multivariate density estimation with arbitrary boundary regions.