Data-dependent kn/-NN estimators consistent for arbitrary processes

S. R. Kulkarni; S. E. Posner; S. Sandilya

doi:10.1109/ISIT.1998.708993

Data-dependent k_n/-NN estimators consistent for arbitrary processes

S. R. Kulkarni, S. E. Posner, S. Sandilya

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

1 Scopus citations

Abstract

Let X₁ , X₂,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with X_i we observe Y_i drawn from an unknown conditional distribution F(y|X_i=x) with continuous regression function m(x)=E[Y|X=·x]. The problem of interest is to estimate Y_n based on X_n and the data {(X_i,Y_i)}i=1 ^n-1. We construct an appropriate data-dependent nearest neighbor estimator and show, with a very elementary proof, that it is consistent for every process X₁,X₂.

Original language	English (US)
Title of host publication	Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998
Pages	388
Number of pages	1
DOIs	https://doi.org/10.1109/ISIT.1998.708993
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

Access to Document

10.1109/ISIT.1998.708993

Cite this

@inproceedings{58376b63f1984c59babd5bbae15690c8,

title = "Data-dependent kn/-NN estimators consistent for arbitrary processes",

abstract = "Let X1 , X2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with Xi we observe Yi drawn from an unknown conditional distribution F(y|Xi=x) with continuous regression function m(x)=E[Y|X=·x]. The problem of interest is to estimate Yn based on Xn and the data {(Xi,Yi)}i=1 n-1. We construct an appropriate data-dependent nearest neighbor estimator and show, with a very elementary proof, that it is consistent for every process X1,X2.",

author = "Kulkarni, {S. R.} and Posner, {S. E.} and S. Sandilya",

year = "1998",

doi = "10.1109/ISIT.1998.708993",

language = "English (US)",

isbn = "0780350006",

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

pages = "388",

booktitle = "Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998",

note = "1998 IEEE International Symposium on Information Theory, ISIT 1998 ; Conference date: 16-08-1998 Through 21-08-1998",

}

Kulkarni, SR, Posner, SE & Sandilya, S 1998, Data-dependent k_n/-NN estimators consistent for arbitrary processes. in Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998., 708993, IEEE International Symposium on Information Theory - Proceedings, pp. 388, 1998 IEEE International Symposium on Information Theory, ISIT 1998, Cambridge, MA, United States, 8/16/98. https://doi.org/10.1109/ISIT.1998.708993

Data-dependent k_n/-NN estimators consistent for arbitrary processes. / Kulkarni, S. R.; Posner, S. E.; Sandilya, S.
Proceedings - 1998 IEEE International Symposium on Information Theory, ISIT 1998. 1998. p. 388 708993 (IEEE International Symposium on Information Theory - Proceedings).

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

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N2 - Let X1 , X2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with Xi we observe Yi drawn from an unknown conditional distribution F(y|Xi=x) with continuous regression function m(x)=E[Y|X=·x]. The problem of interest is to estimate Yn based on Xn and the data {(Xi,Yi)}i=1 n-1. We construct an appropriate data-dependent nearest neighbor estimator and show, with a very elementary proof, that it is consistent for every process X1,X2.

AB - Let X1 , X2,... be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with Xi we observe Yi drawn from an unknown conditional distribution F(y|Xi=x) with continuous regression function m(x)=E[Y|X=·x]. The problem of interest is to estimate Yn based on Xn and the data {(Xi,Yi)}i=1 n-1. We construct an appropriate data-dependent nearest neighbor estimator and show, with a very elementary proof, that it is consistent for every process X1,X2.

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