The general problem of ill conditioning and its role in statistical analysis

The notion of a conditioning analysis of a general, nonlinear set of relations is defined along with an associated definition of ill conditioning. From these, one may identify at least three different kinds of conditioning analyses of interest in statistics and econometrics: data, estimator, and criterion conditioning. While these three coincide in the OLS/linear case, they can and do diverge otherwise. The absence of a general mathematical solution for a conditioning analysis points to computer-intensive alternatives, one of which is suggested and illustrated.