Nonparametric sequential prediction for stationary processes

Gusztáv Morvai; Benjamin Weiss

doi:10.1214/10-AOP576

Nonparametric sequential prediction for stationary processes

Gusztáv Morvai^*, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the problem of finding an universal estimation scheme h_n: R{double-struck}ⁿ → R{double-struck}, n = 1, 2,. .. which will satisfy for all real valued stationary and ergodic processes that are in L^p. We will construct a single such scheme for all 1 < p≤ ∞, and show that for p = 1 mere integrability does not suffice but Llog⁺ L does.

Original language	English
Pages (from-to)	1137-1160
Number of pages	24
Journal	Annals of Probability
Volume	39
Issue number	3
DOIs	https://doi.org/10.1214/10-AOP576
State	Published - May 2011

Keywords

Nonparametric predicton
Stationary processes

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10.1214/10-AOP576

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AB - We study the problem of finding an universal estimation scheme hn: R{double-struck}n → R{double-struck}, n = 1, 2,. .. which will satisfy for all real valued stationary and ergodic processes that are in Lp. We will construct a single such scheme for all 1 < p≤ ∞, and show that for p = 1 mere integrability does not suffice but Llog+ L does.

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KW - Stationary processes

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Nonparametric sequential prediction for stationary processes

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Keywords

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