Unified Statistical Framework for Eliminating Parametric Uncertainty in Applied Mathematical Models via Pivotal and Ancillary Quantities
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Abstract
The technique used here emphasizes pivotal quantities and ancillary statistics relevant for obtaining statistical predictive or confidence decisions for anticipated outcomes of applied stochastic models under parametric uncertainty and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. It does not require the construction of any tables and is applicable whether the experimental data are complete or Type II censored. The proposed technique is based on a probability transformation and pivotal quantity averaging to solve real-life problems in all areas including engineering, science, industry, automation & robotics, business & finance, medicine and biomedicine. It is conceptually simple and easy to use.
Keywords
anticipated outcomes, parametric uncertainty, unknown (nuisance) parameters, pivotal quantities, ancillary statistics, new-sample prediction, within-sample prediction
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How to Cite
Nechval, N., Berzins, G., & Nechval, K. (2025). Unified Statistical Framework for Eliminating Parametric Uncertainty in Applied Mathematical Models via Pivotal and Ancillary Quantities. Research on Intelligent Manufacturing and Assembly, 5(1), 291-312. https://doi.org/10.25082/RIMA.2026.01.001
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
- Nechval NA, Berzins G, Nechval KN, et al. Innovative technique for computing shortest length and/or equal tails confidence intervals in reliability and safety under parametric uncertainty, Pattern Recognition and Information Processing (PRIP 2021): Proceedings of the 15th International Conference, 21–24 Sept. 2021, Minsk, Belarus, pp. 206-210.
- Nechval NA, Berzins G, Nechval KN. A new unified computational method for finding confidence intervals of shortest length and/or equal tails under parametric uncertainty[C]//2021 International Conference on Computational Science and Computational Intelligence (CSCI). IEEE, 2021: 533-539.
- Nechval N, Berzins G, Nechval K. 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. Published online September 24, 2021: 473-482. https://doi.org/10.1007/978-981-16-2377-6_44
- Nechval NA, Berzins G, Nechval KN, et al. A New Intelligent Method for Eliminating Unknown (Nuisance) Parameters from Underlying Models as an Alternative to the Bayesian Approach. Journal of Applied Mathematics and Computation. 2022, 6(1): 53-65. https://doi.org/10.26855/jamc.2022.03.008
- Nechval NA, Berzins G, Nechval KN. Intelligent Computational Approach to Constructing Adequate Statistical Decisions under Parametric Uncertainty of Applied Stochastic Models. 2022 International Conference on Computational Science and Computational Intelligence (CSCI). Published online December 2022: 521-528. https://doi.org/10.1109/csci58124.2022.00098
- Nechval N, Berzins G, Nechval K. Adequate Mathematical Models of the Cumulative Distribution Function of Order Statistics to Construct Accurate Tolerance Limits and Confidence Intervals of the Shortest Length or Equal Tails. WSEAS TRANSACTIONS ON MATHEMATICS. 2023, 22: 154-166. https://doi.org/10.37394/23206.2023.22.20
- Nechval N, Berzins G, Nechval K. Optimal Statistical Estimation and Dynamic Adaptive Control of Airline Seat Protection Levels for Several Nested Fare Classes under Parametric Uncertainty of Customer Demand Models. WSEAS TRANSACTIONS ON MATHEMATICS. 2023, 22: 395-408. https://doi.org/10.37394/23206.2023.22.47
- Nechval NA, Berzins G, Nechval KN. A Unified Technique for Prediction and Optimization of Future Outcomes under Parametric Uncertainty via Pivotal Quantities and Ancillary Statistics. Automatic Control and Computer Sciences. 2023, 57(3): 234-257. https://doi.org/10.3103/s0146411623030070
- Nechval NA, Berzins G, Nechval KN. A novel computational intelligence approach to making efficient decisions under parametric uncertainty of practical models and its applications to Industry 4.0. Advanced Signal Processing for Industry 40, Volume 1. Published online June 1, 2023: 7-1-7-40. https://doi.org/10.1088/978-0-7503-5247-5ch7
- Nicholas Nechval, Berzins G, Nechval K. New Applications of Computational Intelligence for Constructing Predictive or Optimal Statistical Decisions under Parametric Uncertainty. Automatic Control and Computer Sciences. 2023, 57(5): 473-489. https://doi.org/10.3103/s0146411623050085
- Nechval NA, Berzins G, et al. Adequate intelligent constructing predictive or optimal statistical decisions under parametric uncertainty of applied stochastic models. International Journal of Applied Mathematics and Machine Learning. 2023: 43-81. https://doi.org/10.18642/ijamml_7100122268
