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

Abstract

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.

Keywords:

• identification of vector of parameters
• conditioning factors
• Bayes approach
• asymmetrical loss function
• nonparametric estimation
• distribution free method
• numerical algorithm

Acknowledgements

Our heartfelt thanks go to our colleague Dr Aleksander Mazgaj, with whom we commenced the research presented here. With his consent, this text also contains results of joint research. We are also very grateful to Professor Antoni Leon Dawidowicz for his valuable advice and inspiration.

Disclosure statement

No potential conflict of interest was reported by the authors.