Determination of an adequate number of competitive functional models in the square Msplit(q) estimation with the use of a modified Baarda’s approach

The article presents the issue of determining a proper number of competitive functional models in the square Msplit(q) estimation. It is assumed in the theoretical fundamentals of the method of parameter estimation in a split functional model that the observation vector may constitute an unrecognised and unassigned mixture of realisations of several random variables. As such, the observation vector may contain the realisations of a greater number of random variables than the adopted q of the competitive functional models. Too small number q of competitive functional models may leads to breakdown of Msplit(q) estimation. In the theoretical part of the paper, a modified Baarda's test was proposed to detect too small a number of competitive functional models. The idea of the proposed approach is about detection of the observations that should not be assigned to a specific functional model. The efficacy of the proposed strategy was illustrated by two numerical examples.