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## НОВЫЕ КРИТЕРИИ СОГЛАСИЯ ДЛЯ СЕМЕЙСТВА РАСПРЕДЕЛЕНИЙ РЭЛЕЯ, ОСНОВАННЫЕ НА НЕКОТОРОМ СПЕЦИАЛЬНОМ СВОЙСТВЕ И НЕКОТОРОЙ ХАРАКТЕРИЗАЦИИ

Journal of Mathematical Sciences. 2021. Т. 505. С. 230-243.

Ragozin I. A.

In this paper we construct new goodness-of-fit tests for Rayleigh distribution family with an arbitrary scale-parameter σ, based on some property and some characterization. We describe their limiting distributions, calculate local Bahadur efficiencies under close alternatives and perform asymptotic comparison of our test statistics.

И. А. Рагозин, Записки научных семинаров ПОМИ РАН 2020 Т. 495 С. 237-249

In this paper we construct two new goodness-of-fit tests for Pareto Itype distribution family with an arbitrary shape-parameter λ, based on anew characterization. We describe their limit distributions, calculate thelocal Bahadur efficiencies under close alternatives and provide asymptoticcomparison of our test statistics. ...

Added: December 14, 2020

I. A. Ragozin, Journal of Mathematical Sciences 2022 Vol. 268 No. 5 P. 684-692

Based on a new characterization, two new goodness-of-ﬁt tests for Pareto I type distribution family with arbitrary shape-parameter λ are constructed. For these tests, the limiting distributions are described, the local Bahadur eﬃciencies for natural alternatives are calculated, and the asymptotic comparison of test statistics is performed. ...

Added: December 13, 2022

Nikitin Y. Y., Journal of Mathematical Sciences 2014 Vol. 199 No. 2 P. 130-138

We construct several goodness-of-fit tests based on the well-known Puri-Rubin characterization of the power law. Next we find their Bahadur efficiencies under common alternatives and describe the conditions of local asymptotic optimality. ...

Added: January 30, 2015

Nikitin Ya. Yu., Volkova K. Y., Journal of Mathematical Sciences 2015 Vol. 204 No. 1 P. 42-54

We propose new tests of exponentiality of integral and of Kolmogorov type based on a characterization of exponentiality proposed by Ahsanullah. Bahadur efficiency of new tests is computed, conditions of local asymptotic optimality are described. ...

Added: January 30, 2015

Nikitin Y. Y., Volkova K. Y., Journal of Mathematical Sciences 2014 Vol. 199 No. 2 P. 130-138

We construct and study new goodness-of-fit tests for the power distribution based on the Puri-Rubin characterization and using U-empirical distribution functions. We describe their limiting distributions and large deviations. Next we find their local Bahadur efficiency for common alternatives and study the conditions of local optimality. ...

Added: February 10, 2015

Nadezhda Gribkova, Communications in Statistics-Theory and Method 2017 Vol. 46 No. 23 P. 11918-11932

In this article, we establish Cramér-type moderate deviation results for (intermediate) trimmed means Tn = n− 1∑n − mni = kn + 1Xi: n, where Xi: n's are the order statistics corresponding to the first n observations in a sequence X1, X2, … of independent identically distributed random variables with F. We consider two cases of intermediate and heavy trimming. In the former case, when max (αn, βn) → 0 (αn = kn/n, βn = mn/n) and ...

Added: February 28, 2020

Nikitin Y. Y., Volkova K. Y., Mathematical Methods of Statistics 2016 Vol. 25 No. 1 P. 54-66

We build new tests of composite hypothesis of exponentiality which are functionals of U-empirical measures and which are closely related and inspired by some special property of exponential law. We study limiting distributions, large deviations and asymptotic efficiency of new tests. Most favorable alternatives are described. Finally we reject using our test the hypothesis on ...

Added: March 23, 2016

Pavel Pyatov, Povolotsky A. M., Rittenberg V., Journal of Statistical Mechanics: Theory and Experiment 2018 Vol. 2018 No. 053107 P. 1-26

We study the large deviation functions for two quantities characterizing the avalanche dynamics in the Raise and Peel model: the number of tiles removed by avalanches and the number of global avalanches extending through the whole system. To this end, we exploit their connection to the groundstate eigenvalue of the XXZ model with twisted boundary ...

Added: July 17, 2018

Bozin V., Milošević B., Nikitin Y. Y. et al., Bulletin of the Malaysian Mathematical Sciences Society 2020 Vol. 43 No. 1 P. 297-320

Two new symmetry tests, of integral and Kolmogorov type, based on the characterization by squares of linear statistics are proposed. The test statistics are related to the family of degenerate U-statistics. Their asymptotic properties are explored. The maximal eigenvalue, needed for the derivation of their logarithmic tail behavior, was calculated or approximated using techniques from ...

Added: January 4, 2020

Durio A., Y.Y.Nikitin, Statistics and Probability Letters 2016 Vol. 117 No. 10 P. 136-143

The efficiency of distribution-free integrated goodness-of-fit tests was studied by Henze and Nikitin (2000, 2002) under location alternatives. We calculate local Bahadur efficiencies of these tests under more realistic generalized skew alternatives. They turn out to be unexpectedly high. ...

Added: September 16, 2016

Ulyanov V. V., Goetze F., Naumov A., Asymptotic analysis of symmetric functions / . 2015. No. 15025.

In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed. ...

Added: July 13, 2015

Kelbert M., Сухов Ю. М., М. : МЦНМО, 2020

Для освоения теории вероятностей и математической статистики тренировка в решении задач и выработка интуиции важны не меньше, чем
изучение доказательств теорем; большое разнообразие задач по этому предмету затрудняет студентам переход от лекций к экзаменационным задачам,
а от них—к практике. Специфический предмет этого тома, цепи Маркова и их применения,
переживает последнее время большой подъем. Многие замечательные теоретические результаты были ...

Added: February 1, 2021

Gushchin A. A., Valkeila E., Statistics & Decisions 2001 Vol. 19 No. 2 P. 173-190

A characterization of a certain class of exponential experiments, so-called E-experiments, is given. This allows us to give necessary and sufficient conditions for a sequence of experiments to converge to an E-experiment. The obtained results are valid for Gaussian shift experiments. Some asymptotic approximations using E-experiments are studied. ...

Added: October 8, 2013

Pechersky E., Pirogov S. A., Schütz G. M. et al., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 107-120

We study a class of random processes on N particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through ...

Added: December 5, 2020

Yanovich Yury Aleksandrovich, Journal of Mathematics and Statistics 2016 Vol. 12 No. 3 P. 157-175

In many applications, the real high-dimensional data occupy only a very small part in the high dimensional ‘observation space’ whose intrinsic dimension is small. The most popular model of such data is Manifold model which assumes that the data lie on or near an unknown manifold Data Manifold, (DM) of lower dimensionality embedded in an ...

Added: November 24, 2016

Jovanovic M., Milosevic B., Y.Y.Nikitin et al., Computational Statistics & Data Analysis 2015 Vol. 90 P. 100-113

Abstract Two families of scale-free exponentiality tests based on the recent characterization of exponentiality by Arnold and Villasenor are proposed. The test statistics are constructed using suitable functionals of U-empirical distribution functions. The family of integral statistics can be reduced to V- or U-statistics with relatively simple non-degenerate kernels. They are asymptotically normal and have ...

Added: September 3, 2015

Gribkova N., Mathematical Methods of Statistics 2016 Vol. 25 No. 4 P. 313-322

We establish Cramér type moderate deviation results for heavy trimmed L-statistics; we obtain our results under a very mild smoothness condition on the inversion F −1 (F is the underlying distribution function of i.i.d. observations) near two points, where trimming occurs, we assume also some smoothness of weights of the L-statistic. Our results complement previous work on Cramér type large deviations ...

Added: February 28, 2020

Nikitin Y. Y., Kagan A. M., Zaitsev A. Y., Vestnik of the St. Petersburg University: Mathematics 2019 Vol. 52 No. 1 P. 36-53

This is the fourth article in a series of surveys devoted to the scientific achievements of the Leningrad—St. Petersburg School of Probability and Statistics from 1947 to 2017. It is devoted to studies on the characterization of distributions, limit theorems for kernel density estimators, and asymptotic efficiency of statistical tests. The characterization results are related ...

Added: October 1, 2019

Nikitin Ya. Yu., Ahsanullah M., Dordrecht, L., Heidelberg, NY : Springer, 2015

We use the characterization of distribution symmetry in terms of order statistics in order to obtain new tests of symmetry based on U-empirical distribution functions. We calculate their limiting distributions and large deviations and explore their local Bahadur efficiency against location alternatives which turns out to be rather high. ...

Added: April 14, 2015

Поляк Б. Т., Tremba A., Хлебников М. В. et al., Автоматика и телемеханика 2015 № 6 С. 18-41

Исследования переходных режимов в линейных системах при ненулевых начальных условиях были начаты еще в 1948 г. в пионерской работе А.А. Фельдбаума [1]. Однако затем эта линия исследований не получила должного развития; под переходными процессами в основном понимались реакции системы на единичный скачок при нулевых начальных условиях. Существенным прорывом стала статья Р.Н. Измайлова [2], где показана ...

Added: October 18, 2015

Ya. Yu. Nikitin, Metrika 2018 Vol. 81 No. 6 P. 609-618

We consider two scale-free tests of normality based on the characterization of the symmetric normal law by
Ahsanullah, Kibria and Shakil (2014). Both tests have an $U$-empirical structure, but the first one is of integral type, while the second one is of Kolmogorov type. We discuss the limiting behavior of the test statistics and calculate their local ...

Added: October 27, 2018

Gribkova N., Probability and Mathematical Statistics 2017 Vol. 37 No. 1 P. 101-118

In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. (1982) – the first and, as far as we know, the single article where some results ...

Added: February 28, 2020

Nikitin Y. Y., Acta et Commentationes Universitatis Tartuensis de Mathematica 2017 Vol. 21 No. 1 P. 3-24

A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of U-empirical processes. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various ...

Added: November 13, 2017

Grané A., Tchirina, Anna V., Statistics 2013 Vol. 47 No. 1 P. 202-215

We study the efficiency properties of the goodness-of-fit test based on the Q n statistic introduced in Fortiana and Grané [Goodness-of-fit tests based on maximum correlations and their orthogonal decompositions, J. R. Stat. Soc. B 65 (2003), pp. 115–126] using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this ...

Added: September 23, 2014