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sequential hypotheses test; simple hypothesis; optimal stopping; sequential probability ratio test; likelihood ratio statistic; stability inequality

References:

[1] Y. S. Chow, H. Robbins, and D. Siegmund: **Great Expectations: The Theory of Optimal Stopping**. Houghton Mifflin Company, Boston 1971. MR 0331675

[2] E. I. Gordienko and F. S. Salem: **Estimates of stability of Markov control processes with unbounded costs**. Kybernetika 36 (2000), 195–210. MR 1760024

[3] E. I. Gordienko and A. A. Yushkevich: **Stability estimates in the problem of average optimal switching of a Markov chain**. Math. Methods Oper. Res. 57 (2003), 345–365. MR 1990916

[4] P. J. Huber: **A robust version of the probability ratio test**. Ann. Math. Statist. 36 (1965), 1753–1758. MR 0185747 | Zbl 0137.12702

[5] A. Kharin: **On robustifying of the sequential probability ratio test for a discrete model under “contaminations"**. Austrian J. Statist. 3 (2002), 4, 267–277.

[6] A. Kharin: **Robust sequential testing of hypotheses on discrete probability distributions**. Austrian J. Statist. 34 (2005), 2, 153–162.

[7] G. Lorden: **Structure of sequential tests minimizing an expected sample size**. Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. MR 0566323 | Zbl 0407.62055

[8] V. Mackevičius: **Passage to the limit in problems of optimal stopping of Markov processes (in Russian)**. Litovsk. Mat. Sb. (Russian) 13 (1973), 1, 115–128, 236. MR 0347017

[9] R. Montes-de-Oca, A. Sakhanenko, and F. Salem-Silva: **Estimates for perturbations of general discounted Markov control chains**. Appl. Math. 30 (2003), 287–304. MR 2029538

[10] A. Novikov: **Optimal sequential tests for two simple hypotheses**. Sequential Analysis 28 (2009), No. 2. MR 2518830 | Zbl 1162.62080

[11] A. Novikov: **Optimal sequential tests for two simple hypotheses based on independent observations**. Internat. J. Pure Appl. Math. 45 (2008), 2, 291–314. MR 2421867

[12] V. V. Petrov: **Sums of Independent Random Variables**. Springer, New York 1975. MR 0388499 | Zbl 1125.60024

[13] P. X. Quang: **Robust sequential testing**. Ann. Statist. 13 (1985), 638–649. MR 0790562 | Zbl 0588.62136

[14] A. N. Shiryayev: **Statistical Sequential Analysis**. Nauka, Moscow 1969. (In Russian.)

[15] A. Wald and J. Wolfowitz: **Optimum character of the sequential probability ratio test**. Ann. Math. Statist. 19 (1948), 326–339. MR 0026779

[16] J. Whitehead: **The Design and Analysis of Sequential Clinical Trials**. Wiley, New York 1997. MR 0793018 | Zbl 0747.62109