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May 2011 Nonparametric sequential prediction for stationary processes
Gusztáv Morvai, Benjamin Weiss
Ann. Probab. 39(3): 1137-1160 (May 2011). DOI: 10.1214/10-AOP576

Abstract

We study the problem of finding an universal estimation scheme hn : ℝn→ℝ, n=1, 2, … which will satisfy

limt→∞(1/t)∑i=1t|hi(X0, X1, …, Xi−1)−E(Xi|X0, X1, …, Xi−1)|p=0 a.s.

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 L log+L does.

Citation

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Gusztáv Morvai. Benjamin Weiss. "Nonparametric sequential prediction for stationary processes." Ann. Probab. 39 (3) 1137 - 1160, May 2011. https://doi.org/10.1214/10-AOP576

Information

Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1301.60052
MathSciNet: MR2789586
Digital Object Identifier: 10.1214/10-AOP576

Subjects:
Primary: 60G25 , 60G45 , 62G05

Keywords: Nonparametric predicton , Stationary processes

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • May 2011
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