Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors

DOI

10.2991/jsta.2015.14.1.5How to use a DOI?

Keywords

Edgeworth Expansion; parametric bootstrap; t-statistic, linear regression, strongly dependent

Abstract

The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric values, an Edgeworth expansion of the bootstrap t-statistic of arbitrarily large order of the process is proved to have an error of o(n1-s/2) where s is a positive integer. The result is similar to the Edgeworth expansion obtained by Andrews and Lieberman [2002], which was established for the parametric bootstrap t-statistic of the plug-in maximum likelihood (PML) estimators of stationary, Gaussian, and strongly dependent processes, but without the linear regression component.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Mosisa Aga
PY  - 2015
DA  - 2015/03/31
TI  - Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors
JO  - Journal of Statistical Theory and Applications
SP  - 52
EP  - 59
VL  - 14
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2015.14.1.5
DO  - 10.2991/jsta.2015.14.1.5
ID  - Aga2015
ER  -