Robustness of sequential hypotheses testing for heterogeneous independent observations
Authors:
A. Yu. Kharin and T. T. Tu
Journal:
Theor. Probability and Math. Statist. 100 (2020), 169-179
MSC (2010):
Primary 62L10, 62F35
DOI:
https://doi.org/10.1090/tpms/1104
Published electronically:
August 5, 2020
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Additional Information
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.
References
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References
- A. Gut, Probability: A Graduate Course, Springer, New York, 2005. MR 2125120
- Handbook of Sequential Analysis (B. Ghosh and P. K. Sen, eds.), Marcel Dekker, New York, 1991. MR 1174297
- P. Huber, Robust Statistics, John Wiley and Sons, New York, 1981. MR 606374
- A. Kharin, Robust Bayesian prediction under distortions of prior and conditional distributions, J. Math. Sci. 126 (2005), no. 1, 992–997. MR 2160291
- A. Kharin and P. Shlyk, Robust multivariate Bayesian forecasting under functional distortions in the chi-square metric, J. Stat. Plann. Inference 139 (2009), 3842–3846. MR 2553770
- A. Kharin, Performance and robustness evaluation in sequential hypotheses testing, Communications in Statistics — Theory and Methods 45 (2016), no. 6, 1693–1709. MR 3473943
- A. Yu. Kharin, Robustness of sequential testing of hypotheses on parameters of M-valued random sequences, J. Math. Sci. 189 (2013), no. 6, 924–931. MR 3049159
- A. Kharin and Ton That Tu, Performance and robustness analysis of sequential hypotheses testing for time series with trend, Austrian J. Statist. 46 (2017), no. 3–4, 23–36.
- G. G. Kosenko, V. P. Harchenko, and A. G. Kukush, Threshold choice in many-alternative subsequent rule for given mean risk, Radioelectronics and Communications Systems 39 (1996), no. 8, 38–42.
- T. Lai, Sequential analysis: some classical problems and new challenges, Statistica Sinica 11 (2001), no. 2, 303–408. MR 1844531
- P. R. Mercer, Hadamard’s inequality and trapezoid rules for the Riemann–Stieltjes integral, J. Math. Anal. Appl. 344 (2008), 921–926. MR 2426320
- N. Mukhopadhyay, S. Datta, and S. Chattopadhyay, Applied Sequential Methodologies, Marcel Dekker, New York, 2004. MR 2159146
- W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1976. MR 0385023
- A. Wald, Sequential Analysis, John Wiley and Sons, New York, 1947. MR 0020764
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Additional Information
A. Yu. Kharin
Affiliation:
Belarusian State University, Independence Avenue 4, Minsk 220030, Belarus
Email:
kharinay@bsu.by
T. T. Tu
Affiliation:
University of Science and Education, The University of Danang, Danang, Vietnam
Email:
tttu@ued.udn.vn
Keywords:
Truncated sequential test,
heterogeneous observations,
distortions,
robustness,
error probabilities,
expected sample size
Received by editor(s):
March 16, 2019
Published electronically:
August 5, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
