POINTWISE IMPROVEMENT OF MULTIVARIATE KERNEL DENSITY ESTIMATES

Multivariate kernel density estimators are known to systematically dev iate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao-Blackwell's theorem is proposed. Local corrections of kernel density estimators are achiev ed by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance a re investigated and weak and complete consistency are derived under mi ld hypothesis. (C) 1998 Academic Press.