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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2022.03.008

A New Intelligent Method for Eliminating Unknown (Nuisance) Parameters from Underlying Models as an Alternative to the Bayesian Approach

N. A. Nechval1,*, G. Berzins1, K. N. Nechval2, Zh. Tsaurkubule3, M. Moldovan4

1BVEF Research Institute, University of Latvia, Riga, 1586, Latvia. 

2Department of Aviation, Transport and Telecommunication Institute, Riga, 1019, Latvia. 

3Department of Statistics, Baltic International Academy, Riga, 1019, Latvia.

4Department of Biometry, University of Adelaide, Adelaide, 5005, state of South Australia, Australia.

*Corresponding author: N. A. Nechval

Published: March 01, 2022

Abstract

The big question in statistics is: How can we eliminate the unknown (nuisance) parameter from an underlying model? Eliminating unknown (nuisance) parameters from an underlying model is universally recognized as a major problem of statistics and has been formally studied in virtually all approaches to inference. A surprisingly large number of elimination methods have been proposed in the literature on this topic. The classical method of elimination of unknown (nuisance) parameters from the model, which is used repeatedly in the large sample theory of statistics, is to replace the unknown (nuisance) parameter by an estimated value. However, this method is not efficient when dealing with small data samples. The Bayesian approach is dependent of the choice of priors. In this paper, a new method is proposed to eliminate the unknown (nuisance) parameter from the underlying model. This method isolates and eliminates unknown (nuisance) parameters from the underlying model as efficiently as possible. Unlike the Bayesian approach, the proposed method is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate unknown parameters from the problem and to find the efficient statistical decision rules, which often have smaller risk than any of the well-known decision rules. To illustrate the proposed method, some practical applications are given.

Keyword

Underlying model, Parametric uncertainty, Elimination of unknown (nuisance) parameters, Efficient statistical decisions

References

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[2] Nechval, N. A. and Vasermanis, E. K. (2004). Improved Decisions in Statistics, Riga: Izglitibas soli, 2004.

[3] Nechval, N. A., Berzins, G., Purgailis, M., and Nechval, K. N. (2008). Improved estimation of state of stochastic systems via invariant embedding technique, WSEAS Transactions on Mathematics, Vol. 7, 2008, pp. 141-159.

[4] Nechval, N. A., Nechval, K. N., Danovich, V., and Liepins, T. (2011). Optimization of new-sample and within-sample prediction intervals for order statistics, in Proceedings of the 2011 World Congress in Computer Science, Computer Engineering, and Applied Computing, WORLDCOMP'11, Las Vegas Nevada, USA, CSREA Press, July 18-21, 2011, pp. 91-97.

[5] Nechval, N. A., Nechval, K. N., and Berzins, G. (2018). A new technique for intelligent constructing exact g-content tolerance limits with expected (1 − a)-confidence on future outcomes in the Weibull case using complete or Type II censored data, Automatic Control and Computer Sciences (AC&CS), Vol. 52, 2018, pp. 476-488.

[6] Nechval, N. A., Berzins, G., and Nechval, K. N. (2019). Intelligent technique of constructing exact statistical tolerance limits to predict future outcomes under parametric uncertainty for prognostics and health management of complex systems, International Journal of Advances in Computer Science & Its Applications (IJCSIA), Vol. 9, 2019, pp. 30-47.

[7] Nechval, N. A., Berzins, G., Nechval, K. N., and Krasts, J. (2019). A new technique of intelligent constructing unbiased prediction limits on future order statistics coming from an inverse Gaussian distribution under parametric uncertainty, Autom. Control Comput. Sci., Vol. 53, 2019, pp. 223-235.

[8] Nechval, N. A., Berzins, G., and Nechval, K. N. (2019). A novel intelligent technique for product acceptance process optimization on the basis of misclassification probability in the case of log-location-scale distributions, in: F. Wotawa et al. (Eds.), Advances and Trends in Artificial Intelligence. From Theory to Practice. IEA/AIE 2019, Lecture Notes in Computer Science, vol. 11606, 2019, pp. 801-818, Springer Nature Switzerland AG.

[9] Nechval, N. A., Berzins, G., and Nechval, K. N. (2020). A novel intelligent technique of invariant statistical embedding and averaging via pivotal quantities for optimization or improvement of statistical decision rules under parametric uncertainty, WSEAS Transactions on Mathematics, vol. 19, pp. 17-38, 2020.

[10] Nechval, N. A., Berzins, G., Nechval, K. N., and Danovics, V. (2020). A novel technique for optimization of statistical decisions under parametric uncertainty through invariant statistical embedding and averaging in terms of pivotal quantities, Journal of Physics: Conference Series, Vol. 1603, 2020, p. 7, 012022.

[11] Nechval, N. A., Berzins, G., Nechval, K. N., and Danovics, V. (2020). Intelligent constructing optimal airline seat protection levels for multiple nested fare classes of single-leg flights, Journal of Physics: Conference Series, Vol. 1603, 2020, p. 7, 012023.

[12] Nechval, N. A. Berzins, G., and Nechval, K. N. (2020). A new technique of invariant statistical embedding and averaging via pivotal quantities for intelligent constructing efficient statistical decisions under parametric uncertainty, Automatic Control and Computer Sciences, vol. 54, 2020, pp. 191-206.

[13] Nechval, N. A. Berzins, G., and Nechval, K. N. (2020). Cost-effective planning reliability-based inspections of fatigued structures in the case of log-location-scale distributions of lifetime under parametric uncertainty, in Proceed-ings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conference, Edited by Piero Baraldi, Francesco Di Maio and Enrico Zio, ESREL2020-PSAM15, 1-6 November, 2020, Venice, Italy, pp. 455-462.

[14] Nechval, N. A. (2020). Intelligent constructing exact tolerance limits for prediction of future outcomes under parametric uncertainty, in Encyclopedia of Information Science and Technology, Fifth Edition (3 Volumes), USA, IGI Global, pp. 701-729, 2020.

[15] Nechval, N. A., Berzins, G., Nechval, K. N., and Tsaurkubule, Zh. (2021). A novel unified computational approach to constructing shortest-length or equal tails confidence intervals in terms of pivotal quantities and quantile functions, Automatic Control and Computer Sciences, Vol. 55, 2021, pp. 66-84.

[16] Nechval, N. A. Berzins, G., and Nechval, K. N. (2021).  A new technique of invariant statistical embedding and averaging in terms of pivots for improvement of statistical decisions under parametric uncertainty, CSCE'20 - The 2020 World Congress in Computer Science, Computer Engineering, & Applied Computing, July 27-30, 2020,Las Vegas, USA, in:  H. R. Arabnia et al. (eds.), Advances in Parallel & Distributed Processing, and Applications, Transactions on Computational Science and Computational Intelligence, pp. 257-274.  Springer Nature Switzerland AG 2021. 

[17] Nechval, N. A., Berzins, G., and Nechval, K. N. (2021).  A new pivot-based approach to constructing prediction limits and shortest-length or equal tails confidence intervals for future outcomes under parametric uncertainty, Proceedings of the 31st European Safety and Reliability Conference (ESREL 2021), Edited by Bruno Castanier, Marko Cepin, David Bigaud, and Christophe Berenguer,  19-23 September 2021, Angers, France, pp. 2886-2893.  Published by Research Publishing, Singapore, 2021. 

[18] Nechval, N. A., Berzins, G., and Nechval, K. N. (2022).  A new simple computational method of simultaneous constructing and comparing confidence intervals of shortest length and equal tails for making efficient decisions under parametric uncertainty.  Proceedings of Sixth International Congress on Information and Communication Technology – ICICT 2021, Lecture Notes in Network and Systems (LNNS, volume 235), Yang X.-S. , Sherratt S., Dey N., Joshi A. (eds), 25-26 February 2021, London, United Kingdom, pp. 473-482.  Springer Nature Singapore 2022.

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How to cite this paper

A New Intelligent Method for Eliminating Unknown (Nuisance) Parameters from Underlying Models as an Alternative to the Bayesian Approach

How to cite this paper: N. A. Nechval, G. Berzins, K. N. Nechval, Zh. Tsaurkubule, M. Moldovan. (2022) A New Intelligent Method for Eliminating Unknown (Nuisance) Parameters from Underlying Models as an Alternative to the Bayesian Approach. Journal of Applied Mathematics and Computation6(1), 53-65.

DOI: http://dx.doi.org/10.26855/jamc.2022.03.008