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International Journal of Mathematics and Mathematical Sciences
Volume 2017 (2017), Article ID 2045653, 12 pages
Research Article

A Note on the Performance of Biased Estimators with Autocorrelated Errors

Department of Mathematics & Statistics, Banasthali University, Rajasthan 304022, India

Correspondence should be addressed to Gargi Tyagi

Received 31 July 2016; Revised 20 November 2016; Accepted 7 December 2016; Published 30 January 2017

Academic Editor: Weimin Han

Copyright © 2017 Gargi Tyagi and Shalini Chandra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators.