Range Restriction Assumptions Assuming Quadratic Conditional Variances

This paper is concerned with range restriction corrections where (a) the regressions of variables subject to selection on explicit selection variables are linear, and (b) the variance‐covariance matrix of errors of prediction is a quadratic function of the regression estimates. Assumption (b) seems warranted in some data and replaces the homoscedasticity assumption often used in range restriction problems. Computations for range restriction corrections which use assumption (b) are presented. These computations also apply when homoscedasticity applies.