On the lrerror in histogram density estimation: The multidimensional case

Abstract

Under some smoothness and tail conditions on the density the rate of convergence of the expected L₁ error of the classical histogram density estimator is calculated in any dimension. The asymptotic distribution of the standardized L₁ error is derived under minimal conditions. In particular, a sharp uniform rate for the variance of the error is established and explicit representations of the asymptotic variance of the error are given.

Keywords:

• Asymptotic normality
• L₁error
• histogram estimators
• density estimation

AMS 1980 Subject Classification:

• Primary: 62G05
• Secondary: 60F15