# Robert MnatsakanovWest Virginia University | WVU · Eberly College of Arts and Sciences

Robert Mnatsakanov

PhD

## About

50

Publications

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522

Citations

## Publications

Publications (50)

The problem of recovering a moment-determinate multivariate function f via its moment sequence is studied. Under mild conditions on f, the point-wise and L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

We study the problem of approximating the copula and copula density function from a sequence of
transformed moments. In particular, when frequency moments of an underlying bivariate distribution
are available, the uniform convergence of the reconstructed copula and the rate of approximation of
the copula density function are obtained. Finally, the...

The problems of recovering a multivariate function f from the scaled values of its Laplace and Radon transforms are studied, and two novel methods for approximating and estimating the unknown function are proposed. Moreover, using the empirical counterparts of the Laplace transform of the underlying function, a new estimate of the Radon transform i...

This article deals with characterizations of a function in terms of its circular mean Radon transform. We present a new approach (the consistency method) showing how to describe the class of real-valued, planar functions f which have the given circular mean Radon transform Mf over circles centered on the unit circle. Also, expressions are derived f...

New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of [Formula presented]-errors we conducted comparisons of the finite sample performance of...

The problem of recovering quantiles and quantile density functions of a positive random variable via the values of frequency moments is studied. The uniform upper bounds of the proposed approximations are derived. Several simple examples and corresponding plots illustrate the behavior of the recovered approximations. Some applications of the constr...

In this paper, we propose three modified approximations of the ruin probability and the inverse function of the ruin probability using the inversion of the scaled values of Laplace transform suggested by Mnatsakanov et al. (2015). The problem of evaluating numerically the tail-Value at Risk of an insurance portfolio is also discussed briefly. Perfo...

The problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its Laplace transform is studied. Two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed. The uniform and upper bounds of proposed estimates are d...

In this paper three formulas for recovering the conditional mean and conditional variance based on product moments are proposed. The upper bounds for the uniform rate of approximations of regression and derivatives of some moment-determinate function are derived. Two cases where the support of underlying functions is bounded and unbounded from abov...

Two approximations recovering the functions from their transformed moments are proposed. The upper bounds for the uniform rate of convergence are derived. In addition, the comparisons of the estimates of the cumulative distribution function and its density function with the empirical distribution and the kernel density estimates are conducted via a...

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversion...

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample fro...

The problem of recovering the multivariate probability density function ff from the moments of its Radon transform RfRf is studied. The approximation of the Radon transform RfRf itself is obtained from the moments of ff. Under the mild conditions on ff the uniform rates of convergence for the proposed constructions are established.

In this article a new nonparametric density estimator based on the sequence of asymmetric kernels is proposed. This method is natural when estimating an unknown density function of a positive random variable. The rates of Mean Squared Error, Mean Integrated Squared Error, and the L1-consistency are investigated. Simulation studies are conducted to...

An unknown moment-determinate cumulative distribution function or its density function can be recovered from corresponding moments and estimated from the empirical moments. This method of estimating an unknown density is natural in certain inverse estimation models like multiplicative censoring or biased sampling when the moments of unobserved dist...

A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the esti...

Currently three isolated radio pulsars and one binary radio pulsar with no evidence of any previous recycling are known in 97 surveyed Galactic globular clusters (GCs). As pointed out by Lyne et al., the presence of these pulsars cannot be explained by core-collapse supernovae, as commonly assumed for their counterparts in the Galactic disk. We app...

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assump...

The moment-recovered approximations of multivariate distributions are suggested. This method is natural in certain incomplete models where moments of the underlying distribution can be estimated from a sample of observed distribution. This approach is applicable in situations where other methods cannot be used, e.g. in situations where only moments...

We place limits on the population of non-recycled pulsars originating in
globular clusters through Monte Carlo simulations and frequentist statistical
techniques. We set upper limits on the birth rates of non-recycled cluster
pulsars and predict how many may remain in the clusters, and how many may
escape the cluster potentials and enter the field...

We present the first results from a new population study of the radio pulsar content in globular clusters. Our goal is to develop a set of publicly available tools to constrain the underlying population distribution functions based on the sample of 140 pulsars in 26 clusters. In this work, we will present our main statistical techniques and apply t...

The problem of recovering a cumulative distribution function (cdf) and corresponding density function from its moments is studied. This problem is a special case of the classical moment problem. The results obtained within the moment problem can be applied in many indirect models, e.g., those based on convolutions, mixtures, multiplicative censorin...

For estimating the entropy of an absolutely continuous multivariate distribution, we propose nonparametric estimators based
on the Euclidean distances between the n sample points and their k
n
-nearest neighbors, where {k
n
: n = 1, 2, …} is a sequence of positive integers varying with n. The proposed estimators are shown to be asymptotically unb...

The problem of approximation of the moment-determinate cumulative distribution function (cdf) from its moments is studied. This method of recovering an unknown distribution is natural in certain incomplete models like multiplicative-censoring or biased sampling when the moments of unobserved distributions are related in a simple way to the moments...

The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences. Uniform and L1-rates of convergence of moment-recovered pdfs are obtained. Finally, some applications and exampl...

In this paper the well-known insurance ruin problem is reconsidered. The ruin probability is estimated in the case of an unknown
claims density, assuming a sample of claims is given. An important step in the construction of the estimator is the application
of a regularized version of the inverse of the Laplace transform. A rate of convergence in pr...

This paper concerns estimating a probability density function $f$ based on iid observations from $g(x)=W^{-1} w(x) f(x)$, where the weight function $w$ and the total weight $W=\int w(x) f(x) dx$ may not be known. The length-biased and excess life distribution models are considered. The asymptotic normality and the rate of convergence in mean square...

An unknown probability cumulative distribution function (CDF) can be recovered from its moments and estimated from its empirical moments. In this paper, some further results for such moment-empirical CDFs’ are considered, in particular for certain models where the sample is not directly drawn from the distribution of actual interest, as in biased s...

We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on grouping the cells and a kernel type estimator. Inconsistency of the natural estimator and weak consistency of th...

Motivated by problems in linguistics we consider a multinomial random vector for which the number of cells N is not much smaller than the sum of the cell frequencies, i.e. the sample size n. The distribution function of the uniform distribution on the set of all cell probabilities multiplied by N is called the structural distribution function of th...

this report we discuss only the first part of the project. The second one is concerned with the weak convergence results for the likelihood ratio process, while the third part will be devoted to the different sort of estimators b G of a change set without the total boundedness assumption on C.

The classical change-point problem in modern terms, i.e., the mode-change problem, is stated for sufficiently general set-indexed random processes, namely for random measures. A method is shown for solving this problem both in the general form and for the intensity of compound Poisson random measures. The results obtained are novel for the change-p...

The classical change-point problem in modern terms, i.e., the mode-change problem, is stated for sufficiently general set-indexed random processes, namely for random measures. A method is shown for solving this problem both in the general form and for the intensity of compound Poisson random measures. The results obtained are novel for the change-p...

There are a large number of problems in imaging, engineering, physics, etc., where the input-output system is a subject of interest. Namely, the system where one observes the output and is interested in recovering the input signal from the available data. The so-called deconvolution problem is the one which is frequently used in many elds. This typ...

The aim of this article is to construct consistent estimators of the mixing distribution in Poisson mixture models. The case of uncen-sored as well as censored observations is considered. The IMSE is studied and the corresponding rates of convergence are obtained for the proposed estimators.