On error probabilities calculation for the truncated sequential probability ratio test

  • Alexey Y. Kharin Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus
  • Ton That Tu Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Abstract

The truncated sequential probability ratio test of two simple hypotheses is considered for the model of independent non-identically distributed observations. The lower and upper bounds are given for the probability that the necessary number of observations to stop the test does not exceed a preassigned number. New inequalities for the error probabilities of type I and II are obtained to generalize the classic results. New approximations for the error probabilities of type I and II are constructed. The results are applied for the model of time series with trend. In addition, properties of a sequential test based on the least squares method parameter estimate at the moment of truncation are analyzed for the model of time series with trend. Computer experiment results are given.

Author Biographies

Alexey Y. Kharin, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics), docent; associate professor at the department of probability theory and mathematical statistics, faculty of applied mathematics and informatics

Ton That Tu, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

postgraduate student at the department of probability theory and mathematical statistics, faculty of applied mathematics and informatics

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Published
2018-05-05
Keywords: sequential probability ratio test, truncated test, error probabilities, time series with trend
How to Cite
Kharin, A. Y., & Tu, T. T. (2018). On error probabilities calculation for the truncated sequential probability ratio test. Journal of the Belarusian State University. Mathematics and Informatics, 1, 68-76. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/887
Issue
No 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

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