Shrinkage Estimation of Linear Regression Models with GARCH Errors

DOI

10.2991/jsta.2016.15.4.8How to use a DOI?

Keywords

Stein-type shrinkage; likelihood ratio test; linear regression model; GARCH error; asymptotic bias; asymptotic risk.

Abstract

This paper introduces shrinkage estimators for the parameter vector of a linear regression model with con- ditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace. We derive the asymp- totic distributional biases and risks of the shrinkage estimators using a large sample theory. We show that if the shrinkage dimension exceeds two, the relative efficiency of the shrinkage estimator is strictly greater than that of the full model estimator. Furthermore, a Monte Carlo simulation study is conducted to examine the relative performance of the shrinkage estimators with the full model estimator. Our large sample theory and simulation study show that the shrinkage estimators dominate the full model estimator in the entire parameter space. We illustrate the proposed method using a real data set from econometrics.

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  - S. Hossain
AU  - M. Ghahramani
PY  - 2016
DA  - 2016/12/01
TI  - Shrinkage Estimation of Linear Regression Models with GARCH Errors
JO  - Journal of Statistical Theory and Applications
SP  - 405
EP  - 423
VL  - 15
IS  - 4
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2016.15.4.8
DO  - 10.2991/jsta.2016.15.4.8
ID  - Hossain2016
ER  -