vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2018-54-2-179-192vestifm-317Research ArticleМАТЕМАТИКАMATHEMATICSАНАЛИЗ И ИССЛЕДОВАНИЕ РОБАСТНОСТИ ПОСЛЕДОВАТЕЛЬНОГО КРИТЕРИЯ ОТНОШЕНИЯ ВЕРОЯТНОСТЕЙ ДЛЯ МОДЕЛИ НЕЗАВИСИМЫХ НЕОДИНАКОВО РАСПРЕДЕЛЕННЫХ НАБЛЮДЕНИЙPERFORMANCE ANALYSIS AND ROBUSTNESS EVALUATION OF A SEQUENTIAL PROBABILITY RATIO TEST FOR NON-IDENTICALLY DISTRIBUTED OBSERVATIONShttps://orcid.org/0000-0002-5790-1956ХаринА. Ю.KharinA. Yu.

Харин Алексей Юрьевич – кандидат физико-математических наук, доцент, заведующий кафедрой теории вероятностей и математической статистики.

пр. Независимости, 4, 220030, г. Минск.

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.

kharinAY@bsu.byТхат ТуТонThat TuTon

Тон Тхат Ту – соискатель.

пр. Независимости, 4, 220030, г. Минск.

Ton That Tu – Postgraduate Student.

4, Nezavisimosti Ave., 220030, Minsk.

Белорусский государственный университет; Научно-исследовательский институт прикладных проблем математики и информатики.Belarusian State University.Белорусский государственный университет; Педагогический университет Дананга.Belarusian State University.201830062018542179192Copyright © Харин А.Ю., Тхат Ту Т., 20182018Харин А.Ю., Тхат Ту Т.Kharin A.Y., That Tu T.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/317

Рассмотрена проблема последовательного теста для модели независимых неодинаково распределенных наблюдений. На основе рекурсивного расчета построен новый численный подход для аппроксимации тестовых характеристик последовательного критерия отношения вероятностей (ПКОВ) и усеченного ПКОВ (УПКОВ). Исследована проблема анализа робастности, когда «засорение» представлено искажением распределений всех приращений статистики логарифмического отношения правдоподобия. Предложено использование двухсторонних усеченных функций для построения робастного ПКОВ. Указан алгоритм для выбора порогов этих усеченных функций. Результаты применены для последовательной проверки гипотез о параметрах временных рядов с трендом. Для некоторых моделей «засорения» временных рядов с трендом исследована робастность усеченного ПКОВ. Проведенные в работе численные эксперименты подтверждают теоретические выводы.

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.

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The authors declare that there are no conflicts of interest present.