Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2011, Article ID 357814, 9 pages
http://dx.doi.org/10.1155/2011/357814
Research Article

Bayes Estimation of Two-Phase Linear Regression Model

1Department of Statistics, Bhavnagar University, University Campus, Near Gymkhana, Bhavnagar 364002, India
2Department of Mathematics, Bhavnagar University, University Campus, Near Gymkhana, Bhavnagar 364002, India

Received 28 December 2010; Accepted 9 May 2011

Academic Editor: Kwai Sang Chin

Copyright © 2011 Mayuri Pandya et al. 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.

Abstract

Let the regression model be 𝑌𝑖=𝛽1𝑋𝑖+𝜀𝑖, where 𝜀𝑖 are i. i. d. N (0,𝜎2) random errors with variance 𝜎2>0 but later it was found that there was a change in the system at some point of time 𝑚 and it is reflected in the sequence after 𝑋𝑚 by change in slope, regression parameter 𝛽2. The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of 𝑚, 𝛽1,𝛽2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.