On error probabilities calculation for the truncated sequential probability ratio test

Authors

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

Keywords:

sequential probability ratio test, truncated test, error probabilities, time series with trend

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

Issue

No. 1 (2018): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Kharin, A.Y. and 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 (May 2018), 68–76.