CONVERGENCE PROPERTIES OF MULTI-DIMENSIONAL NEAREST NEIGHBOR DENSITY ESTIMATES FOR THE CASE OF GENERAL KERNEL

摘要

In this paper we give weaker conditions to ensure the strong uniform consis-tency of multi-dimensional nearest neighbor (N.N.) estimates with non-uniform kernel andobtain the convergence rates of these estimates on an arbitrary bounded set. The ratescan not be improved in some sense. Obviously, the problem of strong convergence rates ata given point is its special case. The range of applications of estimates is extended.