Asymptotic normality of l1–error in density estimation

Alain Berlinet, Luc Devroye, L. Györfi

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let ƒnbe a histogram estimate constructed from a sample of i.i.d. real-valued random variables with common continuously differentiable density ƒ. In this paper we prove a central limit theorem for the L1 error Ilfn — ƒ||. We determine a positive constant 0 21 — 2/Π in order thatunder the usual conditions of consistencythe law of c. 1995 OPA.

Original languageEnglish
Pages (from-to)329-343
Number of pages15
JournalStatistics
Volume26
Issue number4
DOIs
Publication statusPublished - Jan 1 1995

Fingerprint

Continuously differentiable
Density Estimation
Asymptotic Normality
Central limit theorem
Histogram
Random variable
Estimate
Asymptotic normality
Density estimation
Random variables

Keywords

  • central limit theorem
  • histogram estimate
  • Nonparametric density estimation

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Asymptotic normality of l1–error in density estimation. / Berlinet, Alain; Devroye, Luc; Györfi, L.

In: Statistics, Vol. 26, No. 4, 01.01.1995, p. 329-343.

Research output: Contribution to journalArticle

Berlinet, Alain ; Devroye, Luc ; Györfi, L. / Asymptotic normality of l1–error in density estimation. In: Statistics. 1995 ; Vol. 26, No. 4. pp. 329-343.
@article{eeb80b429d6841c9a6e4be556dbeaa4c,
title = "Asymptotic normality of l1–error in density estimation",
abstract = "Let ƒnbe a histogram estimate constructed from a sample of i.i.d. real-valued random variables with common continuously differentiable density ƒ. In this paper we prove a central limit theorem for the L1 error Ilfn — ƒ||. We determine a positive constant 0 21 — 2/Π in order thatunder the usual conditions of consistencythe law of c. 1995 OPA.",
keywords = "central limit theorem, histogram estimate, Nonparametric density estimation",
author = "Alain Berlinet and Luc Devroye and L. Gy{\"o}rfi",
year = "1995",
month = "1",
day = "1",
doi = "10.1080/02331889508802500",
language = "English",
volume = "26",
pages = "329--343",
journal = "Statistics",
issn = "0233-1888",
publisher = "Taylor and Francis Ltd.",
number = "4",

}

TY - JOUR

T1 - Asymptotic normality of l1–error in density estimation

AU - Berlinet, Alain

AU - Devroye, Luc

AU - Györfi, L.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Let ƒnbe a histogram estimate constructed from a sample of i.i.d. real-valued random variables with common continuously differentiable density ƒ. In this paper we prove a central limit theorem for the L1 error Ilfn — ƒ||. We determine a positive constant 0 21 — 2/Π in order thatunder the usual conditions of consistencythe law of c. 1995 OPA.

AB - Let ƒnbe a histogram estimate constructed from a sample of i.i.d. real-valued random variables with common continuously differentiable density ƒ. In this paper we prove a central limit theorem for the L1 error Ilfn — ƒ||. We determine a positive constant 0 21 — 2/Π in order thatunder the usual conditions of consistencythe law of c. 1995 OPA.

KW - central limit theorem

KW - histogram estimate

KW - Nonparametric density estimation

UR - http://www.scopus.com/inward/record.url?scp=84963167659&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963167659&partnerID=8YFLogxK

U2 - 10.1080/02331889508802500

DO - 10.1080/02331889508802500

M3 - Article

VL - 26

SP - 329

EP - 343

JO - Statistics

JF - Statistics

SN - 0233-1888

IS - 4

ER -