Density estimation from an individual numerical sequence

A. B. Nobel; G. Morvai; S. R. Kulkarni

doi:10.1109/ISIT.1998.708960

Density estimation from an individual numerical sequence

A. B. Nobel, G. Morvai, S. R. Kulkarni

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L₁ consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

Original language	English (US)
Title of host publication	Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998
Pages	355
Number of pages	1
DOIs	https://doi.org/10.1109/ISIT.1998.708960
State	Published - 1998
Event	1998 IEEE International Symposium on Information Theory, ISIT 1998 - Cambridge, MA, United States Duration: Aug 16 1998 → Aug 21 1998

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Other

Other	1998 IEEE International Symposium on Information Theory, ISIT 1998
Country/Territory	United States
City	Cambridge, MA
Period	8/16/98 → 8/21/98

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.1998.708960

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title = "Density estimation from an individual numerical sequence",

abstract = "The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).",

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year = "1998",

doi = "10.1109/ISIT.1998.708960",

language = "English (US)",

isbn = "0780350006",

series = "IEEE International Symposium on Information Theory - Proceedings",

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Nobel, AB, Morvai, G & Kulkarni, SR 1998, Density estimation from an individual numerical sequence. in Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998., 708960, IEEE International Symposium on Information Theory - Proceedings, pp. 355, 1998 IEEE International Symposium on Information Theory, ISIT 1998, Cambridge, MA, United States, 8/16/98. https://doi.org/10.1109/ISIT.1998.708960

TY - GEN

T1 - Density estimation from an individual numerical sequence

AU - Nobel, A. B.

AU - Morvai, G.

AU - Kulkarni, S. R.

PY - 1998

Y1 - 1998

N2 - The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

AB - The article considers univariate density estimation from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known upper bound for the variation of the density an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

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U2 - 10.1109/ISIT.1998.708960

DO - 10.1109/ISIT.1998.708960

M3 - Conference contribution

AN - SCOPUS:84890346426

SN - 0780350006

SN - 9780780350007

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 355

BT - Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998

T2 - 1998 IEEE International Symposium on Information Theory, ISIT 1998

Y2 - 16 August 1998 through 21 August 1998

ER -

Density estimation from an individual numerical sequence

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