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## Goodness-of-Fit Tests for the Power Function Distribution Based on the Puri-Rubin Characterization and Their Efficiencies

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

Nikitin Y. Y., Volkova K. Y.

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.

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

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 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., 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

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

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

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

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

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

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., 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

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 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

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

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

Radionova M. V., Чичагов В. В., Вестник Ижевского государственного технического университета 2014 № 4 (64) С. 151-156

A new class of asymptotic tests is suggested for testing the hypothesis of distribution belonging to the one-parameter exponential family. Each criterion is based on a given set of parametric functions that allow an unbiased estimate. We compared the proposed criterion with criterion is based on the generalized method of moments on the example of ...

Added: January 14, 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

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

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

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

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

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

Radionova M. V., Научно-технический вестник Поволжья 2014 № 6 С. 22-25

The author found the distribution of invariants sample of the general population with half-normal distribution. On the basis of the criterion of shift-scale invariant conducted to test the hypothesis that the set has an exponential distribution against the alternative that the population has a half-normal distribution. The statistical modeling analysis conducted a power. The paper ...

Added: February 9, 2015

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