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## Multivariable Goodness Tests and Approximation of the Residues of Quadratic Forms

Automation and Remote Control. 2010. Vol. 71. No. 7. P. 1346-1357.

Martynov G.

Consideration was given to the omega square Cramer–von Mises tests intended to verify the goodness hypothesis about the distribution of the observed multivariable random vector with the distribution in the unit cube. The limit distribution of the statistics of these tests was defined by the distribution of an infinite quadratic form in the normal random variables. For convenience of computing its distribution, the residue of the quadratic form was approximated by a finite linear combination of the χ2-distributed random variables. Formulas for determination of the residue parameters were established.

Kulagin N. E., L.M. Lerman, Physica D: Nonlinear Phenomena 2023 Vol. 454 Article 133845

We study in this pap er the existence of periodically modulated in one variable and localized in another variable solutions to the cubic Swift-Hohenberg equation on the plane R2. In the first part we try to apply the method by Kirschgassner-Mielke to reduce the problem to the search of finite-dimensional submanifolds with periodic orbits on
them in some formal ...

Added: July 27, 2023

Kreshchuk A., Potapov V. G., Automation and Remote Control 2013 Vol. 74 No. 10 P. 1688-1695

This work is devoted to the problems of information transmission with frequency shift keying and fast frequency hopping in special channels where the signal/noise ratio is low, and a high energy interfering signal is present. We propose a demodulation algorithm that is significantly more stable to the influence of a powerful interfering signal as compared ...

Added: January 30, 2018

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

Alexeeva T., Shirokov N. A., Алгебра и анализ 2024 Т. 36 № 1 С. 40-59

On the chord-arc curve in R^3 classes of functions similar to Hölder functions with smoothness greater than unity are defined. A constructive description of these classes is obtained in terms of the rate of approximation of functions from them by functions that are harmonic in neighborhoods contracting to the curve. The choice of defining these classes ...

Added: January 10, 2024

Silvanovich O. V., Shirokov N. A., Vestnik St. Petersburg University: Mathematics 2018 Vol. 51 No. 3 P. 267-275

For more than a century, the constructive description of functional classes in terms of the possible rate of approximation of its functions by means of functions chosen from a certain set remains among the most important problems of approximation theory. It turns out that the nonuniformity of the approximation rate due between the points of ...

Added: November 26, 2018

Martynov G., Journal of Communications Technology and Electronics 2016 Vol. 61 No. 6 P. 709-716

For more than 60 years, the Anderson–Darling test is most frequently used among all Cramér–von Mises (omega-square) tests. This statistic modifies a classical empirical process defined within the [0, 1] interval by multiplying it by weighting function ψ(t) = (t(1–t))–1/2. The weighting function redistributes the test sensitivity to deviations of the distribution function of the ...

Added: September 16, 2016

Lipovetsky S., Penikas H. I., Model Assisted Statistics and Applications 2020 Vol. 15 P. 285-287

Editorial to the journal special issue devoted to professor Sergei Artemievich Aivazian. ...

Added: January 9, 2021

Igor Kheifets, Velasco C., , in : Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis, Essays in Honor of Halbert L. White Jr. : NY : Springer, 2012. P. 363-382.

This chapter proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct specification of parametric conditional distributions in dynamic discrete choice models, not only of some particular conditional characteristics such as moments or ...

Added: February 23, 2021

Burkov A. A., Shneer S., Turlikov A. M., , in : WAVE ELECTRONICS AND ITS APPLICATION IN INFORMATION AND TELECOMMUNICATION SYSTEMS. 2021. (WECONF 2021) St. Petersburg, Russia, 31 May - 4 June 2021. : IEEE, 2021. Ch. 9470700. P. 1-8.

The development of the Internet of Things technology in cellular networks is considered within the framework of massive machine-type communications with the use of random multiple access algorithms such as ALOHA and its modifications. Despite the fact that this class of algorithms has been studied for a long time, there are no numerical methods for ...

Added: October 28, 2022

Puzino Y. A., Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния 2014 № 22 С. 46-52

The increasing of the efficiency of technological modes of steel products manufacturing requires simulation of metal forming during hot deformation. To obtain correct results, one should set the correct initial and boundary conditions, including the mechanical properties of materials, which represent the dependence of the stress-strain and strain rate at maintained temperature.
In the experiments one ...

Added: January 19, 2015

М. : Национальный исследовательский университет "Высшая школа экономики", 2022

Added: January 12, 2023

Высоцкий Л. И., Журнал вычислительной математики и математической физики 2021 Т. 61 № 5 С. 776-786

Tensorizations of functions are studied, that is, tensors with elements 𝐴(𝑖1,…,𝑖𝑑)=𝑓(𝑥(𝑖1,…,𝑖𝑑)) 𝐴(𝑖1,…,𝑖𝑑)=𝑓(𝑥(𝑖1,…,𝑖𝑑)), where 𝑓(𝑥) is some function defined on an interval and {𝑥(𝑖1,…,𝑖𝑑)} is a grid on this interval. For tensors of this type, the problem of approximation by tensors admitting a tensor train (ТТ) decomposition with low ТТ ranks is posed. For the class ...

Added: October 31, 2021

Mkhitarian V., Sirotin V., Вопросы статистики 2015 № 03 С. 81-83

The history, the program and the main results of the conference on multivariate statistics methods and their applications are presented in the paper. Main feature of the conference is the great variety of the discussed issues. Along with scientific research the problems of statistical education were discussed at the round table. ...

Added: March 16, 2015

Шагай М. А., Shirokov N. A., Записки научных семинаров ПОМИ РАН 2023 Т. 527 С. 242-255

Let sk, 1 6 k 6 m, m > 2, be disjoint segments lying in a parallelogram Q. We denote by ℘(z) a doubly periodic Weierstrass function with the fundamental parallelogram Q. Let fk : sk → C be functions, and let f 0 k ∈ L pk (sk), 1 6 k 6 m, 1 ...

Added: February 10, 2024

Bielsko-Biala : ATH University, 2013

В монографии представлены методы, подходы и стратегии развития предприятий. ...

Added: November 30, 2014

Чирухин В. А., Записки Горного института 2014 Т. 208 С. 197-202

In the article the methods of processing of statistical data about periodic process by the least squares method with usage of Bessel functions and Fourie numbers are analyzed. The simple method for approximation with a choice of the fluctuation period, proceeding from a minimum of the estimated error is offered. ...

Added: October 31, 2017

Martynov G., , in : Festschrift in honor of Paul Deheuvels. : Springer, 2014.

In statistical applications it is often assumed that an observed random process is Gaussian. We propose a statistical method for testing the null hypothesis that an observed random process on the interval $[0,1]$ is a mean zero Gaussian process with specified covariance function. Our method is based on a finite number of observations of the ...

Added: March 23, 2014

Bliznets Ivan, Cygan M., Komosa P. et al., , in : Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Vol. 60.: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2016. Ch. 3. P. 1-17.

The H-free Edge Deletion problem asks, for a given graph G and integer k, whether it is possible to delete at most k edges from G to make it H-free, that is, not containing H as an induced subgraph. The H-free Edge Completion problem is defined similarly, but we add edges instead of deleting them. ...

Added: October 31, 2018

Yashunsky A., Algebra Universalis 2019 Vol. 80 No. 1 (5) P. 1-16

We consider the problem of approximating distributions of Bernoulli random variables by applying Boolean functions to independent random variables with distributions from a given set. For a set B of Boolean functions, the set of approximable distributions forms an algebra, named the approximation algebra of Bernoulli distributions induced by B. We provide a complete description ...

Added: September 9, 2020

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

Balakrishnan A., Moinak M., Indian Journal of Finance 2017 Vol. 11 No. 6 P. 21-35

This paper evaluated the cross sectional relationship between firm characteristics : size and value with risks and expected returns in the Indian stock market on different horizon of time from previous studies. Furthermore, the study deployed different breakpoints for market capitalization (median, market capitalization, and BSE breakpoints) and price to book ratio (equal weighted and ...

Added: September 9, 2018

Salnikov A., Stepanova I., Gudkova T. et al., , in : 2021 14th International Conference Management of large-scale system development (MLSD). : IEEE, 2021. P. 1-3.

We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...

Added: October 30, 2022

Yashunsky A., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 1 P. 217-221

We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions ...

Added: July 6, 2021

Lazarev A. A., Lemtyuzhnikova D. V., Tyunyatkin A. A. et al., IFAC-PapersOnLine 2022 Vol. 55 No. 10 P. 2881-2886

This research extends the interpolation approach to approximating the objective function value for the minimization maximum lateness problem. The interpolation approach is defined using a special objective function Lmax(α), which is proven to be continuous and depends only on α transform coefficient. Such a function is proven to be monotonically increasing, and this property is ...

Added: December 5, 2022