Title: On the asymptotic normality of the l(1)-errors and l(2)-errors in histogram density-estimation
Authors: Beirlant, Jan ×
Gyorfi, L
Lugosi, G #
Issue Date: 1994
Publisher: Canadian journal statistics
Series Title: Canadian journal of statistics-revue canadienne de statistique vol:22 issue:3 pages:309-318
Abstract: The L1- and L2-errors of the histogram estimate of a density f from a sample X1, X2,..., X(n) using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Gyorfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).
ISSN: 0319-5724
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Statistics Section
× corresponding author
# (joint) last author

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