Relative stability of global errors of nonparametric function estimators

This paper presents relative stability properties of various nonparametric density estimators (histogram, kernel estimates) and of regression estimators (partitioning, kernel, and nearest neighbor estimates). In density estimation, let En denote the L/sub 1/ error of an estimate calculated from n data, whereas in regression estimation, the L/sub 2/ error of the estimate is used. Sufficient conditions for E/sub n//E{E/sub n/}/spl rarr/1 in probability are provided. If this limit holds, the asymptotic behavior of the random error E/sub n/ can be characterized by its expectation E{E/sub n/},, and one may apply, for example, the established rate-of-convergence results for E{En}.