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Vladimir Panov

Publications and source records attributed to Vladimir Panov.

16 recordsLinked to original sources
arXiv2026

Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond

This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class of rational-infinitely divisible distributions. We propose an estimation framework based on band-limited kernels, which are the functions characterized by compactly supported Fourier transform. Under mild assumptions, the proposed estimators are theoretically shown to achieve polynomial (and in some cases even almost parametric) convergence rates. Finally, we demonstrate the numerical performance of the algorithm on simulated examples.

stat.ME↗
arXiv2026

Statistical Inference for Quasi-Infinitely Divisible Distributions via Fourier Methods

This study focuses on statistical inference for the class of quasi-infinitely divisible (QID) distributions, which was recently introduced by Lindner, Pan and Sato (2018). The paper presents a Fourier approach, based on the analogue of the L{é}vy-Khintchine theorem with a signed spectral measure. We prove that for some subclasses of QID distributions, the considered estimates have polynomial rates of convergence. This is a remarkable fact when compared to the logarithmic convergence rates of similar methods for infinitely divisible distributions, which cannot be improved in general. We demonstrate the numerical performance of the algorithm using simulated examples.

stat.ME↗
arXiv2025

Decompounding Under General Mixing Distributions

This study focuses on statistical inference for compound models of the form $X=ξ_1+\ldots+ξ_N$, where $N$ is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables $ξ_1, ξ_2, \ldots$. The paper addresses the problem of reconstructing the distribution of $ξ$ from observed samples of $X$'s distribution, a process referred to as decompounding, with the assumption that $N$'s distribution is known. This work diverges from the conventional scope by not limiting $N$'s distribution to the Poisson type, thus embracing a broader context. We propose a nonparametric estimate for the density of $ξ$, derive its rates of convergence and prove that these rates are minimax optimal for suitable classes of distributions for $ξ$ and $N$. Finally, we illustrate the numerical performance of the algorithm on simulated examples.

math.ST↗
arXiv2024

Statistical Inference for Scale Mixture Models via Mellin Transform Approach

This paper deals with statistical inference for the scale mixture models. We study an estimation approach based on the Mellin -- Stieltjes transform that can be applied to both discrete and absolute continuous mixing distributions. The accuracy of the corresponding estimate is analysed in terms of its expected pointwise error. As an important technical result, we prove the analogue of the Berry -- Esseen inequality for the Mellin transforms. The proposed statistical approach is illustrated by numerical examples.

stat.ME↗
arXiv2022

Modelling the Bitcoin prices and the media attention to Bitcoin via the jump-type processes

In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Lévy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the low-frequency setup, which is for the Lévy - based models essentially more difficult than the high-frequency case. We design a semiparametric estimation procedure for the statistical inference on the parameters and the Lévy measures of the considered processes. We show that the dynamics of the market attention can be effectively modelled by the Lévy processes with finite Lévy measures, and propose a data-driven procedure for the description of the Bitcoin prices.

q-fin.ST↗
arXiv2021

Extreme value analysis for mixture models with heavy-tailed impurity

This paper deals with the extreme value analysis for the triangular arrays, which appear when some parameters of the mixture model vary as the number of observations grow. When the mixing parameter is small, it is natural to associate one of the components with "an impurity" (in case of regularly varying distribution, "heavy-tailed impurity"), which "pollutes" another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher-Tippett-Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

math.ST↗
arXiv2020

Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimates

In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main theorem yields the asymptotic representation of the corresponding distribution function with exponentially decaying remainder term. This result can be efficiently used for studying the projection density estimates, based, for instance, on Legendre polynomials. More precisely, we construct the sequence of accompanying laws, which approximates the distribution of maximal deviation of the considered estimates with polynomial rate. Moreover, we construct the confidence bands for densities, which are honest at polynomial rate to a broad class of densities.

math.PR↗
arXiv2018

Limit Theorems for the Alloy-type Random Energy Model

In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, while the second has the mean \(\sqrt{n}a\) with some \(a\in \R,\) and the variance \(σ\ne 1\). The phase space \((a,σ) \subset \R \times \R_+\) is divided onto several domains, where after appropriate normalisation, the partition function converges in law to the stable distribution. These domains are separated by the critical surfaces, corresponding to transitions from the normal distribution to \(α-\)stable with \(α\in (1,2)\), after to 1-stable, and finally to \(α-\)stable with \(α\in (0,1).\) The corresponding phase diagram is the central result of this paper.

math.PR↗
arXiv2017

Semiparametric estimation in the normal variance-mean mixture model

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 the corresponding mixing distribution. We illustrate the performance of our procedure on simulated and real data.

stat.OT↗
arXiv2017

Limit theorems for sums of random variables with mixture distribution

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions of the sums due to various relations between these parameters.

math.PR↗
arXiv2016

Low frequency estimation of continuous-time moving average Lévy processes

In this paper we study the problem of statistical inference for a continuous-time moving average Lévy process of the form $$Z_{t} = \int_{\mathbb{R}}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}$$ with a deterministic kernel (\K\) and a L{é}vy process (L\). Especially the estimation of the Lévy measure (ν\) of $L$ from low-frequency observations of the process $Z$ is considered. We construct a consistent estimator, derive its convergence rates and illustrate its performance by a numerical example. On the technical level, the main challenge is to establish a kind of exponential mixing for continuous-time moving average Lévy processes.

math.ST↗
arXiv2016

Convergence rates of maximal deviation distribution for projection estimates of Lévy densities

In this paper, we consider projection estimates for Lévy densities in high-frequency setup. We give a unified treatment for different sets of basis functions and focus on the asymptotic properties of the maximal deviation distribution for these estimates. Our results are based on the idea to reformulate the problems in terms of Gaussian processes of some special type and to further analyze these Gaussian processes. In particular, we construct a sequence of excursion sets, which guarantees the convergence of the deviation distribution to the Gumbel distribution. We show that the rates of convergence presented in previous articles on this topic are logarithmic and construct the sequences of accompanying laws, which approximate the deviation distribution with polynomial rate.

math.PR↗
arXiv2015

Statistical inference for generalized Ornstein-Uhlenbeck processes

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-ξ_{t}} \left( X_{0} + \int_{0}^{t} e^{ξ_{u-}} d u \right), \] where \(ξ_s\) is a L{é}vy process. Our primal goal is to estimate the characteristics of the Lévy process \(ξ\) from the low-frequency observations of the process \(X\). We present a novel approach towards estimating the L{é}vy triplet of \(ξ,\) which is based on the Mellin transform technique. It is shown that the resulting estimates attain optimal minimax convergence rates. The suggested algorithms are illustrated by numerical simulations.

stat.ME↗
arXiv2015

Series representations for bivariate time-changed L{é}vy models

In this paper, we analyze a L{é}vy model based on two popular concepts - subordination and L{é}vy copulas. More precisely, we consider a two-dimensional L{é}vy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some L{é}vy copula. We prove a series representation for our model, which can be efficiently used for simulation purposes, and provide some practical examples based on real data

math.ST↗
arXiv2013

Statistical inference for exponential functionals of Lévy processes

In this paper, we consider the exponential functional \(A_{\infty}=\int_0^\infty e^{-ξ_s}ds\) of a L{é}vy process \(ξ_s\) and aim to estimate the characteristics of \(ξ_{s}\) from the distribution of \(A_{\infty}\). We present a new approach, which allows to statistically infer on the L{é}vy triplet of \(ξ_{t}\), and study the theoretical properties of the proposed estimators. The suggested algorithms are illustrated with numerical simulations.

stat.OT↗