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Uniform consistency of the partitioning estimate under ergodic conditions

Part of: Limit theorems Inference from stochastic processes Nonparametric inference

Published online by Cambridge University Press:  09 April 2009

Naâmane Laib
Naâmane Laib
Affiliation:
L.S.T.A. Université Paris 6 Aile 45-55, 3ème étage 4, Place Jussieu 75252 Paris Cedex 05 France e-mail: [email protected]
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Abstract

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We establish the uniform almost sure convergence of the partitioning estimate, which is a histogram-like mean regression function estimate, under ergodic conditions for a stationary and unbounded process. The main application of our results concerns time series analysis and prediction in the Markov processes case.

Keywords

Autoregressionergodic processesmartingale differencepartitioning estimatepredictionregressionstationarity.

MSC classification

Secondary: 62G05: Estimation 60F15: Strong theorems 62M10: Time series, auto-correlation, regression, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 1 , August 1999 , pp. 1 - 14
Copyright
Copyright © Australian Mathematical Society 1999

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