Theory of Probability and Mathematical Statistics
Robustness of sequential hypotheses testing for heterogeneous independent observations
A. Yu. Kharin, T. T. Tu
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Abstract: The problem of robustness for truncated sequential tests of two simple hypotheses is considered for the model of heterogeneous independent observations under distortions. An approach for performance characteristics calculation is proposed. Asymptotic analysis of robustness is performed. A family of robustified sequential tests is constructed. Numerical examples illustrate the theoretical results.
Keywords: Truncated sequential test, heterogeneous observations, distortions, robustness, error probabilities, expected sample size.
Bibliography: 1. A. Gut, Probability: a graduate course, Springer, New York, 2005.
2. Handbook of sequential analysis, (B. Ghosh, P. K. Sen, ed.), Marcel Dekker, New York, 1991.
3. P. Huber, Robust statistics, John Wiley and Sons, New York, 1981.
4. A. Kharin, Robust Bayesian prediction under distortions of prior and conditional distributions, Journal of Mathematical Sciences, 126 (2005), no. 1, 992–997.
5. A. Kharin, P. Shlyk, Robust multivariate Bayesian forecasting under functional distortions in the chi-square metric, Journal of Statistical Planning and Inference, 139 (2009), 3842–3846.
6. A. Kharin, Performance and robustness evaluation in sequential hypotheses testing, Communications in Statistics – Theory and Methods, 45 (2016), no.6, 1693–1709.
7. A. Yu. Kharin, Robustness of sequential testing of hypotheses on parameters of M-valued random sequences, Journal of Mathematical Sciences, 189 (2013), no. 6, 924–931.
8. A. Kharin, Ton That Tu, Performance and robustness analysis of sequential hypotheses testing for time series with trend, Austrian Journal of Statistics, 46 (2017), no.3-4, 23–36.
9. G. G. Kosenko, V. P. Harchenko, A. G. Kukush, Threshold choice in many-alternative subsequent rule for given mean risk, Radioelectronics and Communications Systems, 39(1996), no. 8, 38–42.
10. T. Lai, Sequential analysis: some classical problems and new challenges, Statistica Sinica, 11(2001), no. 2, 303–408.
11. P. R. Mercer, Hadamard’s inequality and trapezoid rules for the Riemann–Stieltjes integral, Journal of Mathematical Analysis and Applications, 344 (2008), 921–926.
12. N. Mukhopadhyay, S. Datta, S. Chattopadhyay, Applied sequential methodologies, Marcel Dekker, New York, 2004.
13. W. Rudin, Principles of mathematical analysis, McGraw-Hill, USA, 1976.
14. A. Wald, Sequential analysis, John Wiley and Sons, New York, 1947.