Statistical sequential hypotheses testing on para meters of probability distributions of random binary data
Abstract
An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.
References
- Mukhopadhyay N, de Silva B. Sequential methods and their applications. Boca Raton: CRC Press; 2009. 409 p.
- Lai TL. Sequential analysis: some classical problems and new challenges. Statistica Sinica. 2001;11:303–408.
- Wald A. Sequential analysis. New York: John Wiley and Sons; 1947. 212 p.
- Aivazian SA. Comparison of optimal properties of the tests of Neyman – Pearson and Wald. Teoriya veroyatnostei i ee primeneniya. 1959;4(1):86–93. Russian.
- Huber PJ, Ronchetti EM. Robust statistics. New York: Wiley; 2009. 354 p.
- Maevskii VV, Kharin YuS. Robust regressive forecasting under functional distortions in a model. Automation and Remote Control. 2002;63(11):1803–1820. DOI: 10.1023/A:1020959432568.
- Kemeny JG, Snell JL. Finite Markov Chains. New York: D. Van Nostrand Co.; 1960. 210 p.
- Kharin AY. Robastnost’ baiesovskikh i posledovatel’nykh statisticheskikh reshayushchikh pravil [Robustness of Bayesian and sequential statistical decision rules]. Minsk: Belarusian State University; 2013. 207 p. Russian.
- Kharin A, Tu TT. Performance and robustness analysis of sequential hypotheses testing for time series with trend. Austrian Journal of Statistics. 2017;46(3–4):23–36. DOI: 10.17713/ajs.v46i3-4.668.
- Tu TT, Kharin AY. Sequential probability ratio test for many simple hypotheses on parameters of time series with trend. Journal of the Belarusian State University. Mathematics and Informatics. 2019;1:35–45. DOI: 10.33581/2520-6508-2019-1-35-45.
- Kharin AY. An approach to asymptotic robustness analysis of sequential tests for composite parametric hypotheses. Journal of Mathematical Sciences. 2017;227(2):196–203. DOI: 10.1007/s10958-017-3585-z.
- Kharin AY, Tu TT. On error probability calculation for the truncated sequential probability ratio test. Journal of the Belarusian State University. Mathematics and Informatics. 2018;2018(1):68–76. Russian.
Copyright (c) 2021 Journal of the Belarusian State University. Mathematics and Informatics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The authors who are published in this journal agree to the following:
- The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
- The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
- The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)
