Estimation of regression coefficient of a selected population

Estimation of parameters of a selected population is a very well-studied problem. To date all researchers have discussed the problem of estimation of either the location parameters or the scale parameters of the selected population(s). In this article this problem is extended to the problem of estimation of the regression coefficient of the selected bivariate population. For two linear regression models it is demonstrated that the problem of estimation of the regression coefficient of the selected regression line can be reduced to the problem of estimation of the mean of the selected population as studied by Dahiya (1974). These theoretical results are applied in portfolio theory and corporate finance. It is our expectation that development of theoretical results in this direction will enhance the applicability of the results on estimation after selection. Copyright © 2013 Grace Scientific Publishing, LLC.