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NEW GOODNESS-OF-FIT TESTS FOR PARETO I TYPE DISTRIBUTION, BASED ON SOME CHARACTERIZATION
Journal of Mathematical Sciences. 2022. Vol. 268. No. 5. P. 684-692.
I. A. Ragozin
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.
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
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
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
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
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
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
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
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 ...
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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., 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
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
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
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
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., 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
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
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
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Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
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Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
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Added: November 1, 2019