The problem of estimation of the regression parameters in several simple regression models
with measurement errors is considered when it is suspected that the regression lines may
be parallel with some degree of uncertainty. In this regard we propose five estimators,
namely, (i) the unrestricted estimator, (ii) the restricted estimator, (iii) the preliminary test
estimator, (iv) the Stein-type estimator and (v) the positive-rule Stein-type estimator as
in Saleh (2006). Properties of these estimators are studied in an asymptotic set up and
the asymptotic distributional bias, MSE matrices, and risk under a quadratic loss function
are obtained based on a sequence of local alternatives and dominance properties of these
estimators are provided.