Statistical Estimation - OLS Estimation

One simple measure of how badly S(q) fits S is to examine the sum of squared elements of Esamp = S - S(q). The function is known as the Ordinary Least Squares (OLS) discrepancy function, and may be written


where Tr() denotes the trace operator. The values in q which, for a given S, minimize FOLS are called Ordinary Least Squares (OLS) estimates. That is


The OLS discrepancy function has a number of difficulties, summarized nicely by Everitt (1984). In particular, it is not scale free — different scalings of the manifest variables can produce different discrepancy function values. Moreover, when calculated on sample discrepancies, simple sums of squares may be inappropriate from a statistical standpoint, because the elements of S are not independent random variables, and because they usually have different sampling variances.