L∞ Error and Bandwidth Selection for Kernel Density Estimates of Large Data

Abstract

Kernel density estimates are a robust way to reconstruct a continuous distribution from a discrete point set. Typically their effectiveness is measured either in L1 or L2 error. In this paper we investigate the challenges in using L ∞ (or worst case) error, a stronger measure than L1 or L2. We present efficient solutions to two linked challenges: how to evaluate the L ∞ error between two kernel density estimates and how to choose the bandwidth parameter for a kernel density estimate built on a subsample of a large data set. 1 1