On piecewise linear density estimators

J. Beirlant, A. Berlinet and L. Györfi

Statistica Neerlandica, 1999, vol. 53, issue 3, 287-308

Abstract: We study piecewise linear density estimators from the L1 point of view: the frequency polygons investigated by Scott (1985) and Jones et al. (1997), and a new piecewise linear histogram. In contrast to the earlier proposals, a unique multivariate generalization of the new piecewise linear histogram is available. All these estimators are shown to be universally L1 strongly consistent. We derive large deviation inequalities. For twice differentiable densities with compact support their expected L1 error is shown to have the same rate of convergence as have kernel density estimators. Some simulated examples are presented.

Date: 1999
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