Minimum Chi-Square vs Least Squares in Grouped Data

Abstract

Estimation of parameters from grouped data is considered using a least squares estimator popular in sceintific applications. The method minimizes the square distance between the empirical and hypothesized cumulative distribution functions, and is reminiscent of a discrete version of the Cramer-von Mises statistic. The resulting least squares estimator, is related to the minimum chi-square estimator, and likewise is asymptotically normal. The two methods are compared briefly for categorized mixed lognormal data with a jump at zero.