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Automatic Control and Computer Sciences

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01.09.2021

Intelligent Constructing Efficient Statistical Decisions via Pivot-Based Elimination of Unknown (Nuisance) Parameters from Underlying Models

verfasst von: N. A. Nechval, G. Berzins, K. N. Nechval, Zh. Tsaurkubule

Erschienen in: Automatic Control and Computer Sciences | Ausgabe 5/2021

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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.

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Fraser, D.A.S., Sufficient statistics with nuisance parameters, Ann. Math. Stat., 1956, vol. 27, no. 3, pp. 838–842. https://doi.org/10.1214/aoms/1177728191MathSciNetCrossRefMATH

Cox, D.R., Some problems connected with statistical inference, Ann. Math. Stat., 1958, vol. 29, no. 2, pp. 357–372. https://doi.org/10.1214/aoms/1177706618MathSciNetCrossRefMATH

Linnik, Yu.V., On the elimination of nuisance parameters in statistical problems, in Proc. 5th Berkeley Symp. on Math. Statistics and Probability, 1965, vol. 1, pp. 267–280.

Dawid, A.P., On the concepts of sufficiency and ancillarity in the presence of nuisance parameters, J. R. Stat. Soc., Ser. B (Methodol.), 1975, vol. 37, no. 2, pp. 248–258. https://doi.org/10.1111/j.2517-6161.1975.tb01540.xCrossRefMATH

Basu, D., On the elimination of nuisance parameters, J. Am. Stat. Assoc., 1977, vol. 72, no. 358, pp. 355–366. https://doi.org/10.1080/01621459.1977.10481002MathSciNetCrossRefMATH

Nechval, N.A. and Vasermanis, E.K., Improved Decisions in Statistics, Riga: Izglitibas Soli, 2004.

Nechval, N.A., Berzins, G., Purgailis, M., and Nechval, K.N., Improved estimation of state of stochastic systems via invariant embedding technique, WSEAS Trans. Math., 2008, vol. 7, no. 4, pp. 141–159.MathSciNet

Nechval, N.A., Nechval, K.N., Danovich V., and Liepins, T., Optimization of new-sample and within-sample prediction intervals for order statistics, in Proc. 2011 World Congress in Computer Science, Computer Engineering, and Applied Computing, WORLDCOMP'11, Las Vegas, 2011, Las Vegas: CSREA Press, pp. 91–97.

Nechval, N.A., Nechval, K.N., and Berzins, G., A new technique for intelligent constructing exact γ-content tolerance limits with expected (1 – α)-confidence on future outcomes in the Weibull case using complete or type II censored data, Autom. Control Comput. Sci., 2018, vol. 52, no. 6, pp. 476–488. https://doi.org/10.3103/S0146411618060081CrossRef

10.

Nechval, N.A., Berzins, G., and Nechval, K.N., Intelligent technique of constructing exact statistical tolerance limits to predict future outcomes under parametric uncertainty for prognostics and health management of complex systems, Int. J. Adv. Comput. Sci. Its Appl., 2019, vol. 9, pp. 30–47.

11.

Nechval, N.A., Berzins, G., Nechval, K.N., and Krasts, J., 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., 2019, vol. 53, no. 3, pp. 223–235. https://doi.org/10.3103/S0146411619030088CrossRef

12.

Nechval, N.A. Berzins, G., and Nechval, K.N., A novel intelligent technique for product acceptance process optimization on the basis of misclassification probability in the case of log-location-scale distributions, in Advances and Trends in Artificial Intelligence. From Theory to Practice. IEA/AIE 2019, Wotawa, F., Friedrich, G., Pill, I., Koitz-Hristov, R., and Ali, M., Eds., Lecture Notes in Computer Science, vol. 11606, Cham: Springer, 2019, pp. 801–818. https://doi.org/10.1007/978-3-030-22999-3_68CrossRef

13.

Nechval, N.A., Berzins, G., and Nechval, K.N. 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 Trans. Math., 2020, vol. 19, pp. 17–38.CrossRef

14.

Nechval, N.A., Berzins, G., Nechval, K.N., and Danovics, V., A novel technique for optimization of statistical decisions under parametric uncertainty through invariant statistical embedding and averaging in terms of pivotal quantities, J. Phys.: Conf. Ser., 2020, vol. 1603, p. 012022. https://doi.org/10.1088/1742-6596/1603/1/012022CrossRef

15.

Nechval, N.A., Berzins, G., Nechval, K.N., and Danovics, V., Intelligent constructing optimal airline seat protection levels for multiple nested fare classes of single-leg flights, J. Phys.: Conf. Ser., 2020, vol. 1603, p. 012023. https://doi.org/10.1088/1742-6596/1603/1/012023CrossRef

16.

Nechval, N.A., Berzins, G., and Nechval, K.N., A new technique of invariant statistical embedding and averaging in terms of pivots for improvement of statistical decisions under parametric uncertainty, in Proc. 2020 World Congress in Computer Science, Computer Engineering, and Applied Computing (CSCE 2020), Las Vegas, 2020 (in press).

17.

Nechval, N.A., Berzins, G., and Nechval, K.N., A new technique of invariant statistical embedding and averaging via pivotal quantities for intelligent constructing efficient statistical decisions under parametric uncertainty, Autom. Control Comput. Sci., 2020, vol. 54, no. 3, pp. 191–206. https://doi.org/10.3103/S0146411620030049CrossRef

18.

Nechval, N.A. Berzins, G., and Nechval, K.N., Cost-effective planning reliability-based inspections of fatigued structures in the case of log-location-scale distributions of lifetime under parametric uncertainty, in Proc. 30th Europ. Safety and Reliability Conf. and 15th Probabilistic Safety Assessment and Management Conf., ESREL2020-PSAM15, Venice, 2020, Baraldi, P., Di Maio, F., and Zio, E., Eds., pp. 455–462.

19.

Nechval, N.A., Intelligent constructing exact tolerance limits for prediction of future outcomes under parametric uncertainty, in Encyclopedia of Information Science and Technology, Khosrow-Pour, M., Ed., IGI Global, 2021, 5th ed., pp. 701–729. https://doi.org/10.4018/978-1-7998-3479-3.ch049CrossRef

20.

Nechval, N.A., Berzins, G., Nechval, K.N., and Tsaurkubule, Zh., A novel unified computational approach to constructing shortest-length or equal tails confidence intervals in terms of pivotal quantities and quantile functions, Autom. Control Comput. Sci., 2021, vol. 55, no. 1, pp. 66–84. https://doi.org/10.3103/S0146411621010065CrossRef

21.

Nechval, N.A. Berzins, G., and Nechval, K.N., A new technique of invariant statistical embedding and averaging in terms of pivots for improvement of statistical decisions under parametric uncertainty, in Advances in Parallel & Distributed Processing, and Applications. CSCE 2020, Arabnia, H.R., et al., Eds., Transactions on Computational Science and Computational Intelligence, Cham: Springer, 2021, pp. 263–281.

Titel: Intelligent Constructing Efficient Statistical Decisions via Pivot-Based Elimination of Unknown (Nuisance) Parameters from Underlying Models
verfasst von: N. A. Nechval
G. Berzins
K. N. Nechval
Zh. Tsaurkubule
Publikationsdatum: 01.09.2021
Verlag: Pleiades Publishing
Erschienen in: Automatic Control and Computer Sciences / Ausgabe 5/2021
Print ISSN: 0146-4116
Elektronische ISSN: 1558-108X
DOI: https://doi.org/10.3103/S0146411621050060

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