Bayes Estimation of Two-Phase Linear Regression Model

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.