О комбинаторном усиленном законе больших чисел и ранговых статистиках
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https://doi.org/10.21638/spbu01.2020.311Аннотация
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Библиографические ссылки
Литература
1. von Bahr B. Remainder term estimate in a combinatorial central limit theorem // Z. Wahrsch. verw. Geb. 1976. Vol. 35. P. 131–139.
2. Ho S. T., Chen L.H.Y. An Lp bounds for the remainder in a combinatorial central limit theorem // Ann. Probab. 1978. Vol. 6. P. 231–249.
3. Bolthausen E. An estimate of the remainder in a combinatorial central limit theorem // Z. Wahrsch. verw. Geb. 1984. Vol. 66. P. 379–386.
4. Goldstein L. Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing // J. Appl. Probab. 2005. Vol. 42. P. 661–683. https://doi.org/10.1239/jap/1127322019
5. Neammanee K., Suntornchost J. A uniform bound on a combinatorial central limit theorem // Stoch. Anal. Appl. 2005. Vol. 23. P. 559–578. https://doi.org/10.1081/SAP-200056686
6. Neammanee K., Rattanawong P. A constant on a uniform bound of a combinatorial central limit theorem // J. Math. Research. 2009. Vol. 1. P. 91–103. https://doi.org/10.5539/jmr.v1n2p91
7. Chen L.H.Y., Fang X. On the error bound in a combinatorial central limit theorem // Bernoulli. 2015. Vol. 21, N1. P. 335–359. https://doi.org/10.3150/13-BEJ569
8. Frolov A.N. Esseen type bounds of the remainder in a combinatorial CLT // J. Statist. Planning and Inference. 2014. Vol. 149. P. 90–97. https://doi.org/10.1016/j.jspi.2014.01.004
9. Frolov A.N. Bounds of the remainder in a combinatorial central limit theorem // Statist. Probab. Letters. 2015. Vol. 105. P. 37–46. https://doi.org/10.1016/j.spl.2015.05.020
10. Фролов А.Н. О вероятностях умеренных уклонений комбинаторных сумм // Вестник С.- Петерб. ун-та. Сер. 1. Математика. Механика. Астрономия. 2015. Т. 2 (60). Вып. 1. C. 60–67.
11. Frolov A.N. On large deviations of combinatorial sums. 2019. ArXiv: 1901.04244.
12. Frolov A.N. On Esseen type inequalities for combinatorial random sums // Communications in Statistics - Theory and Methods. 2017. Vol. 46. Iss. 12. P. 5932–5940. https://doi.org/10.1080 /03610926.2015.1115074
13. Frolov A.N. On a combinatorial strong law of large numbers // Istatistik: Journ. of Turkish Statist. Assoc. 2018. Vol. 11, no. 3. P. 46–52. Available at: http://jtsa.ieu.edu.tr/current/1.pdf (accessed: May 26, 2020).
14. Гаек Я., Шидак З. Теория ранговых критериев. М.: Наука, 1971.
15. Большев Л.Н., Смирнов Н.В. Таблицы математической статистики. М.: Наука, 1983.
16. Фролов А.Н. Краткий курс теории вероятностей и математической статистики. СПб.: Лань, 2017.
References
1. von Bahr B., “Remainder term estimate in a combinatorial central limit theorem”, Z. Wahrsch. verw. Geb. 35, 131–139 (1976).
2. Ho S.T., Chen L.H.Y., “An Lp bounds for the remainder in a combinatorial central limit theorem”, Ann. Probab. 6, 231–249 (1978).
3. Bolthausen E., “An estimate of the remainder in a combinatorial central limit theorem”, Z. Wahrsch. verw. Geb. 66, 379–386 (1984).
4. Goldstein L., “Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing”, J. Appl. Probab. 42, 661–683 (2005). https://doi.org/10.1239/jap/1127322019
5. Neammanee K., Suntornchost J., “A uniform bound on a combinatorial central limit theorem”, Stoch. Anal. Appl. 23, 559–578 (2005). https://doi.org/10.1081/SAP-200056686
6. Neammanee K., Rattanawong P., “A constant on a uniform bound of a combinatorial central limit theorem”, J. Math. Research 1, 91–103 (2009). https://doi.org/10.5539/jmr.v1n2p91
7. Chen L.H.Y., Fang X., “On the error bound in a combinatorial central limit theorem”, Bernoulli, 21(1), 335–359 (2015). https://doi.org/10.3150/13-BEJ569
8. Frolov A.N., “Esseen type bounds of the remainder in a combinatorial CLT”, J. Statist. Planning and Inference 149, 90–97 (2014). https://doi.org/10.1016/j.jspi.2014.01.004
9. Frolov A.N., “Bounds of the remainder in a combinatorial central limit theorem”, Statist. Probab. Letters 105, 37–46 (2015). https://doi.org/10.1016/j.spl.2015.05.020
10. Frolov A.N., “On the probabilities of moderate deviations for combinatorial sums”, Vestnik St. Petersburg University. Mathematics 48, iss. 1, 23–28 (2015). https://doi.org/10.3103/S1063454115010045
11. Frolov A.N., “On large deviations of combinatorial sums” (2019). ArXiv: 1901.04244.
12. Frolov A.N., “On Esseen type inequalities for combinatorial random sums”, Communications in Statistics - Theory and Methods 46(12), 5932–5940 (2017). https://doi.org/10.1080/03610926.2015.1115074
13. Frolov A.N., “On a combinatorial strong law of large numbers”, Istatistik: Journ. of Turkish Statist. Assoc. 11(3), 46–52 (2018). Available at: http://jtsa.ieu.edu.tr/current/1.pdf (accessed: May 26, 2020).
14. Hajek J., Sidak Z., Theory of rank tests (Nauka Publ., Moscow, 1971). (In Russian)
15. Bol’shev L.N., Smirnov N.V., Tables of mathematical statistics (Nauka Publ., Moscow, 1983). (In Russian)
16. Frolov A.N., Short course of probability theory and mathematical statistics (Lan’ Publ., St.Petersburg, 2017). (In Russian)
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Опубликован
04.09.2020
Как цитировать
Фролов, А. Н. (2020). О комбинаторном усиленном законе больших чисел и ранговых статистиках. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия, 7(3), 490–499. https://doi.org/10.21638/spbu01.2020.311
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Математика
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Статьи журнала «Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия» находятся в открытом доступе и распространяются в соответствии с условиями Лицензионного Договора с Санкт-Петербургским государственным университетом, который бесплатно предоставляет авторам неограниченное распространение и самостоятельное архивирование.
