Some pitfalls in the use of Minimum Chi Square

Abstract

Estimation according to the criterion of minimum chi square (MCS) was introduced by Kirstine Smith in 1916 and later mentioned by Kendall and Stuart as an alternative to the methods based on least squares (LS) and maximum likelihood (ML). In the paper attention is called to the fact that the statistic Q which is the one actually minimized is only approximately χ2 and that the later introduced statistic G by minimization produces estimates identical with ML estimates. G is also approximated by χ2 (thus by Q, too). A so trivial difference as the one between two approximations does not seem sufficiently important to base an alternative method of estimation on.