Conditional Parameter Identification with Asymmetrical Losses of Estimation Errors

In many scientific and practical tasks, the classical concepts for parameter identification are satisfactory and generally applied with success, although many specialized problems necessitate the use of methods created with specifically defined assumptions and conditions. This paper investigates the method of parameter identification for the case where losses resulting from estimation errors can be described in polynomial form with additional asymmetry representing different results of under- and overestimation. Most importantly, the method presented here considers the conditionality of this parameter, which in practice means its significant dependence on other quantities whose values can be obtained metrologically. To solve a problem in this form the Bayes approach was used, allowing a minimum expected value of losses to be achieved. The methodology was based on the nonparametric technique of statistical kernel estimators, which freed the worked out procedure from forms of probability distributions characterizing both the parameter under investigation and conditioning quantities. As a result, a ready to direct use algorithm has been presented here.