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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 154646 Total View: 1845505
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2020.12.012

A New Unified Computational Approach to Intelligent Constructing Shortest-Length or Equal Tails Confidence Intervals under Parametric Uncertainty

N. A. Nechval 1,*, G. Berzins 1, K. N. Nechval 2, Zh. Tsaurkubule 3

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

2 Transport and Telecommunication Institute, Riga, 1019, Latvia.

3 Baltic International Academy, Riga, 1019, Latvia.

*Corresponding author: N. A. Nechval

Published: December 11,2020

Abstract

A confidence interval is a range of values that gives the user a sense of how pre-cisely a statistic estimates a parameter. In the present paper, a novel unified com-putational approach is proposed to construct shortest-length or equal tails confi-dence intervals in terms of pivotal quantities and quantile functions. In statistics, a pivotal quantity (or pivot) is a function of observations and unobservable parameters such that the function’s probability distribution does not depend on the unknown parameters (including nuisance parameters). This approach represents a simple and computationally attractive numerical method for finding the shortest-length or equal tails confidence intervals using the pivotal quantities, which are developed from either maximum likelihood estimates or sufficient statistics. Finding a pivotal quantity is not discussed, but the choice a “good” pivotal quantity is essential for the resulting confidence interval to be useful. The unified computational approach yields intervals in several situations which have previously required separate analyses using more advanced techniques and tables for numerical solutions. Unlike the Bayesian approach, the proposed approach is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate nuisance parameters from the problem via the technique of invariant statistical embedding and averaging in terms of pivotal quantities (ISE&APQ). To illustrate the proposed approach, numerical examples are given. In detail, the Pareto distribution is discussed.

References

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[10] Nechval, N. A., Berzins, G., & 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. Wo-tawa et al. (Eds.), Advances and Trends in Artificial Intelligence. From Theory to Practice.IEA/AIE 2019, Lecture Notes in Computer Science, vol. 11606, pp. 801-818, Springer Nature Switzerland AG, 2019.

[11] Nechval, N. A., Berzins, G., & 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.

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

How to cite this paper

A New Unified Computational Approach to Intelligent Constructing Shortest-Length or Equal Tails Confidence Intervals under Parametric Uncertainty

How to cite this paper: N. A. Nechval, G. Berzins, K. N. Nechval, Zh. Tsaurkubule. (2020) A New Unified Computational Approach to Intelligent Constructing Shortest-Length or Equal Tails Confidence Intervals under Parametric Uncertainty. Journal of Applied Mathematics and Computation, 4(4), 206-223.

DOI: http://dx.doi.org/10.26855/jamc.2020.12.012