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Nonparametric statistical inference for compound models
Statistics. 2024. Vol. 58. No. 4. P. 943–960.
This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables \(\xi_1+...+\xi_N\), where the number of summands, \(N\), is a random variable independent of \(\xi_1, \xi_2,...\) Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of \(N\), assuming that the distribution of \(\xi\) is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of \(N\) is not necessarily of Poisson type.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Belomestny D., Morozova E., Panov V., Bernoulli: a journal of mathematical statistics and probability 2026 Vol. 32 No. 2 P. 1481–1502
This study focuses on statistical inference for compound models of the form \(X=\xi_1+\ldots+\xi_N\), where \(N\) is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables \(\xi_1, \xi_2, \ldots\). The paper addresses the problem of reconstructing the distribution of \(\xi\) from observed samples of \(X\)'s distribution, a process ...
Added: July 24, 2025
Belomestny D., Morozova E., Panov V., / Series arXiv.org "math.ST". 2024. No. 2405.05419.
This study focuses on statistical inference for compound models of the form \(X=\xi_1+\ldots+\xi_N\), where \(N\) is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables \(\xi_1, \xi_2, \ldots\). The paper addresses the problem of reconstructing the distribution of \(\xi\) from observed samples of \(X\)'s distribution, a process ...
Added: May 10, 2024
Синцова К. А., https://ms.hse.ru/voronovo2019, 2019.
В данной работе исследуется модельная задача о стационарных вынужденных колебаниях жидкости при высокой частоте в поле силы тяжести в бесконечном бассейне с коническим дном. Получаются оценки малых установившихся гравитационных колебаний жидкости в окрестности конической точки и на бесконечности. ...
Added: December 6, 2019
Belomestny D., Panov V., Statistics 2018 Vol. 52 No. 3 P. 571–589
In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers nonparametrically the density of ...
Added: January 19, 2018
Belomestny D., Panov V., Woerner J., Bernoulli: a journal of mathematical statistics and probability 2019 Vol. 25 No. 2 P. 902–931
In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form
\[ Z_{t}=\int_{\R}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}, \] with a deterministic kernel \(\K\) and a L{\'e}vy process \(L\). Especially the estimation of the L\'evy measure \(\nu\) of $L$ from low-frequency observations of the process $Z$ is considered. We construct ...
Added: December 9, 2017
Belomestny D., Panov V., / Series ArXiv.org "Stat". 2017. No. 1705.07578.
In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers nonparametrically the density of ...
Added: May 23, 2017
Belomestny D., Panov V., Woerner J., / Series arXiv "math". 2016. No. 1607.00896.
In this paper we study the problem of statistical inference for a continuous time moving average L\'evy process \(Z\) observed at low-frequency. We construct a consistent estimator for the L\'evy triplet of \(Z\), derive its convergence rates and prove their optimality. The performance of our estimation procedure is illustrated by numerical example. ...
Added: July 5, 2016