Observed data based estimator and both observed data and prior information based estimator under asymmetric losses

Hoque, Zahirul and Wesolowski, Jacek and Khan, Shahjahan (2007) Observed data based estimator and both observed data and prior information based estimator under asymmetric losses. American Journal of Mathematical and Management Sciences, 27 (1/ 2). pp. 93-110. ISSN 0196-6324

Abstract

In Bayesian approach of statistical analyses we incorporate the prior information about the parameter of the model with the observed data. This prior information is in the form of a prior distribution of the parameter. If the prior information is available as a constant value of the parameter rather than its' prior distribution, the Bayesian approach cannot be pursued. However, there are estimation methods that incorporate such prior information with the observed data. The expectation is that the incorporation of such additional information in the estimation process would result in a better estimator than that based on the observed data alone. In some cases this may be true, but in many other cases the risk of worse consequences cannot be ruled out. This paper studies the performance of the observed data based unrestricted estimator (UE), and both observed data and prior information based preliminary test estimator (PTE) of the univariate normal mean under the linex loss function. The risk functions of both UE and PTE are derived. The moment generating function (MGF) of PTE is derived which turns out to be a component of the risk function. From the MGF the first two moments of PTE are obtained and found to be identical to that obtained by using different approaches in Khan and Saleh (2001) and Zellner (1986). Under the linex loss criterion the performance of the PTE is compared with that of UE. It is revealed that if the uncertain non-sample prior information about the value of the mean is not too far from its true value, PTE outperforms UE.


Statistics for USQ ePrint 3787
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Full text reference: Hoque, Z., Wosolowiski, J. and Khan, S. (2007). Observed data based estimator and both observed and prior information based estimator under asymmetric losses. American Journal of Mathematical and Management Sciences, Vol 27 No 1 & 2, 93-110. Access restricted: publisher does not allow re-distribution of work.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 25 Jan 2008 04:10
Last Modified: 02 Jul 2013 22:57
Uncontrolled Keywords: asymmetric loss; non-sample prior information; maximum likelihood and preliminary test estimators; risk function
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
URI: http://eprints.usq.edu.au/id/eprint/3787

Actions (login required)

View Item Archive Repository Staff Only