Bayes Parameter Identification with Polynomial Asymmetrical Loss Function

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 here. The Bayes decision rule allowing to minimize potential losses is used. Calculation algorithms are based on the nonparametric methodology of statistical kernel estimators, which frees the method from distribution type. Three basic cases are considered in detail: a linear, a quadratic, and finally a general concept for a higher order 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.