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## Efficiency of Exponentiality Tests Based on a Special Property of Exponential Distribution

Mathematical Methods of Statistics. 2016. Vol. 25. No. 1. P. 54-66.

Nikitin Y. Y., Volkova K. Y.

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 exponentiality of the lengths of reigns of Roman emperors which has been actively discussed last years.

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

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

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

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

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

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

V.V. Litvinova, Ya. Yu. Nikitin, Journal of Mathematical Sciences 2016 Vol. 219 No. 5 P. 782-788

Some new U-empirical tests for normality of Kolmogorov type based on the famous Polya's characterization are build and explored. Their local asymptotic efficiency in Bahadur sense is calculated. ...

Added: November 5, 2016

Ragozin I. A., Записки научных семинаров ПОМИ РАН 2021 Т. 505 С. 230-243

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. ...

Added: November 29, 2021

Nikitin Y. Y., Ragozin I. A., Vestnik St. Petersburg University: Mathematics 2019 Vol. 52 No. 2 P. 169-177

The logistic family of distributions belongs to the class of important families in the theory of probability and mathematical statistics. However, the goodness-of-fit tests for the composite hypothesis of belonging to the logistic family with unknown location parameter against the general alternatives have not been sufficiently explored. We propose two new goodness-of-fit tests: the integral ...

Added: October 1, 2019

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

Mariani M., Probability Theory and Related Fields 2010 Vol. 147 No. 3–4 P. 607-648

Large deviations principles for a family of scalar 1 + 1 dimensional conservative stochastic PDEs (viscous conservation laws) are investigated, in the limit of jointly vanishing noise and viscosity. A first large deviations principle is obtained in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions ...

Added: December 4, 2017

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 Y., Proceedings of Machine Learning Research 2017 Vol. 60 P. 18-38

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: June 15, 2017

Mariani M., Zambotti L., Advances in Applied Probability 2016 Vol. 48 No. 3 P. 648-671

A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of ...

Added: December 10, 2017

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

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

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

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Borzykh D., ЛЕНАНД, 2021

Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...

Added: February 20, 2021

В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80

Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...

Added: May 3, 2017

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148

In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...

Added: May 17, 2017