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Estimation of the Parameters of two Parallel Regression Lines Under Uncertain Prior Information
Author(s) -
Khan Shahjahan
Publication year - 2003
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200290017
Subject(s) - estimator , statistics , mathematics , linear regression , regression analysis , a priori and a posteriori , regression , sample (material) , polynomial regression , computer science , philosophy , chemistry , epistemology , chromatography
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.