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Exact moderate and large deviations for linear random fields

Part of: Limit theorems Distribution theory Stochastic processes

Published online by Cambridge University Press:  26 July 2018

Hailin Sang  and
Yimin Xiao
Hailin Sang*
Affiliation:
The University of Mississippi
Yimin Xiao*
Affiliation:
Michigan State University
*
* Postal address: Department of Mathematics, The University of Mississippi, University, MS 38677, USA. Email address: sang@olemiss.edu
** Postal address: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA. Email address: xiao@stt.msu.edu
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Abstract

By extending the methods of Peligrad et al. (2014), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.

Keywords

Large deviationmoderate deviationlinear random fieldnonparametric regressionDavis–Gut law of the iterated logarithm

MSC classification

Primary: 60F10: Large deviations 60G60: Random fields 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 431 - 449
Copyright
Copyright © Applied Probability Trust 2018 

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