PERFORMANCE ANALYSIS AND ROBUSTNESS EVALUATION OF A SEQUENTIAL PROBABILITY RATIO TEST FOR NON-IDENTICALLY DISTRIBUTED OBSERVATIONS
https://doi.org/10.29235/1561-2430-2018-54-2-179-192
Abstract
In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters
of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.
About the Authors
A. Yu. Kharin
Belarusian State University.
Belarus
Belarus
Alexey Yu. Kharin – Ph. D. (Physics and Mathematics), Associate Professor, Head of the Department of Probability Theory and Mathematical Statistics.
4, Nezavisimosti Ave., 220030, Minsk.
Ton That Tu
Belarusian State University.
Viet Nam
Viet Nam
Ton That Tu – Postgraduate Student.
4, Nezavisimosti Ave., 220030, Minsk.
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