Abstract
In this chapter, a new technique of invariant embedding of sample statistics in a decision criterion (performance index) and averaging this criterion via pivotal quantities (pivots) is proposed for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging in terms of pivotal quantities (ISE&APQ) 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 risks than any of the well-known decision rules. The aim of this chapter is to show how the technique of ISE&APQ may be employed in the particular case of optimization, estimation, or improvement of statistical decisions under parametric uncertainty. To illustrate the proposed technique of ISE&APQ, application examples are given.
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References
N.A. Nechval, E.K. Vasermanis, Improved Decisions in Statistics (Izglitibas soli, Riga, 2004)
N.A. Nechval, G. Berzins, M. Purgailis, K.N. Nechval, Improved estimation of state of stochastic systems via invariant embedding technique. WSEAS Trans. Math. 7, 141–159 (2008)
N.A. Nechval, K.N. Nechval, V. Danovich, T. Liepins, 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
N.A. Nechval, K.N. Nechval, G. Berzins, 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. (AC&CS) 52, 476–488 (2018)
N.A. Nechval, G. Berzins, K.N. Nechval, 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. Appl. (IJCSIA) 9, 30–47 (2019)
R.H. Berk, A special group structure and equivariant estimation. Ann. Math. Stat. 38, 1436–1446 (1967)
T.S. Ferguson, Mathematical Statistics (Academic Press, New York, 1967)
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Nechval, N.A., Berzinsh, G., 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. In: Arabnia, H.R., et al. Advances in Parallel & Distributed Processing, and Applications. Transactions on Computational Science and Computational Intelligence. Springer, Cham. https://doi.org/10.1007/978-3-030-69984-0_20
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DOI: https://doi.org/10.1007/978-3-030-69984-0_20
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