Estimation of Intercept and Slope of Several Straight Lines : The Parallelism Problem

M.S.H. Khan (1995). Estimation of Intercept and Slope of Several Straight Lines : The Parallelism Problem. Journal of Statistical Research, Vol. 29, No. 2, pp. 79-88.

Abstract

Consider several straight lines : $y_{ij}=\theta_i+\beta_jt_{ij}+e_{ij}$ $(i=1,\ldots,p$ and $j=1,\ldots,n_i)$ . In many practical situations, such as bioassay problem, one may suspect homogeneity of the regression slopes i.e., $\beta_1=\beta_2=\cdots=\beta_p$ . Under this situation, this paper considers the estimation of the parameters $\theta=(\theta_1,\ldots,\theta_p)'$ and $\beta=(\beta_1,\ldots,\beta_p)'$ respectively. Four reasonable estimators of $\theta$ and $\beta$ are proposed and their optimality properties under MSE comparisons are evaluated. The paper basically presents a unified theory of preliminary test approach to shrinkage estimators for the problem and suggest their preference for use.