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On piecewise linear density estimators
Author(s) -
Beirlant J.,
Berlinet A.,
Györfi L.
Publication year - 1999
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00113
Subject(s) - mathematics , estimator , piecewise , histogram , piecewise linear function , differentiable function , kernel (algebra) , rate of convergence , convergence (economics) , statistics , mathematical analysis , combinatorics , computer science , image (mathematics) , computer network , channel (broadcasting) , artificial intelligence , economics , economic growth
We study piecewise linear density estimators from the L 1 point of view: the frequency polygons investigated by S cott (1985) and J ones 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 L 1 strongly consistent. We derive large deviation inequalities. For twice differentiable densities with compact support their expected L 1 error is shown to have the same rate of convergence as have kernel density estimators. Some simulated examples are presented.