PARAMETER IDENTIFICATION FOR ASYMMETRICAL POLYNOMIAL LOSS FUNCTION

Abstract

The parameter identification for problems where losses arising from overestimation and underestimation are different and can be described by an asymmetrical and polynomial function is investigated in this paper. The Bayes decision rule allowing to minimize potential losses is used. Calculation algorithms are based on the nonparametric methodology of statistical kernel estimators, which releases the method from dependence on distribution type. Three basic cases are considered in detail: a linear, a quadratic, and finally a general concept for a higher degree polynomial – here the cube-case is described in detail as an example. For each of them, the final result constitutes a numerical procedure enabling to effectively calculate the optimal value of a parameter in question, presented in its complete form which demands neither detailed knowledge of the theoretical aspects nor laborious research of the user. Although the above method was investigated from the point of view of automatic control problems, it is universal in character and can be applied to a wide range of tasks, also outside the realm of engineering.