Estimation of the Parameters of two Parallel Regression Lines Under Uncertain Prior Information

The problem of parallelism for bi-linear regression lines arises in many real life investigations. For two linear regression models with normal errors, the estimation of the slope as well as the intercept parameters is considered when it is apriori suspected that the two lines are parallel. Three different estimators are defined by using both the sample data and the non-sample uncertain prior information. The relative performances of the unrestricted, restricted and preliminary test estimators are investigated based on the analysis of the bias, and risk functions under quadratic loss. An example based on a medical study is used to illustrate the method.