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Cramér type moderate deviations for random fields

Part of: Distribution theory Limit theorems Stochastic processes

Published online by Cambridge University Press:  12 July 2019

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

We study the Cramér type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric regression with random field errors.

Keywords

Cramér type moderate deviationlong range dependencenonparametric regressionspatial linear processrandom field

MSC classification

Primary: 60F10: Large deviations 60G60: Random fields 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 223 - 245
Copyright
© Applied Probability Trust 2019 

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