An algorithm for conditional multidimensional parameter identification with asymmetric and correlated losses of under- and overestimations

摘要

Many of today's specialized applicational tasks are obliged to consider the influence of inevitable errors in the identification of parameters appearing in a model. Favourable results can also be achieved through measuring, and then accounting for definite (e.g. current) values of factors which show a significant reaction to the values of those parameters. This paper is dedicated to the problem of the estimation of a vector of parameters, where losses resulting from their under- and overestimation are asymmetric and mutually correlated. The issue is considered from a supplementary conditional aspect, where particular coordinates of conditioning variables may be continuous, discrete, multivalued (in particular binary) or categorized (ordered and unordered). The final result is a ready-to-use algorithm for calculating the value of an estimator, optimal in the sense of minimum expectation of losses using a multidimensional asymmetric quadratic function, for practically any distributions of describing and conditioning variables.