On comparing several populations with a control population
It is shown that a popular variable choice method of Hellwig, which is recommended in the Polish econometric textbooks does not enjoy a very basic consistency property. It means in particular that the method may lead to rejection of significant variables in econometric modeling. A simulation study and a real data analysis case are given to support theoretical results.
In the paper it is shown that exponential families of probabilities have the quadratic derivative of the likelihood ratio, and explicit formulas for this derivative are derived.