Maximum Likelihood Estimation of a Linear Regression Function with Grouped Data

The maximum likelihood estimation of a linear regression function calls for considerable computational effort when the data are grouped. For large samples, a simple alternative to the fully grouped solution has been proposed by Fryer and Pethybridge and necessitates placing the data at the mid‐points of equal intervals and obtaining the approximate mid‐point (a.m.p.) solution and then applying simple computable grouping‐corrections to this estimate. This paper examines the performance of the alternative solution for small samples corresponding to a range of regressions. Depending on the group widths, the alternative solution is acceptable for samples of less than 100 observations. Some slight non‐detectable departures from the standard assumptions (e.g. normality of data) are shown not to affect the acceptance of the alternative solution as an adequate approximation of the grouped solution. Finally, consideration is given to the regression problem in which the data are given in unequal width intervals, and new grouping‐corrections are derived to bring the a.m.p. solution back into line with the fully grouped solution.