Recovery of functions from moments with applications
Title: Recovery of functions from moments with applications
Speaker: Dr. Robert Mnatsakanov
Professor, Department of Mathematics, West Virginia University Yonsei University
Date and time:
Friday, January 30, 2026
11:00 A.M. – 12:00 P.M. Eastern Time
Nguyen Engineering Building, Jajodia Auditorium, Room 1101
4511 Patriot Circle, Fairfax, Virginia 22030
The seminar talk is also live-streamed.
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Abstract:
In this talk the problem of recovering the moment-determinate functions and their derivatives given the information contained in the sequence of moments is discussed. It is shown how the rate of approximations is related to the number of moments used in proposed constructions.
Moment type reconstructions are of interest in many areas of mathematics and statistics. For example, as one of the main applications in statistics, we will show how our approximations, based on estimated moments of the model, yields a new type of non-parametric estimates of the quantile, conditional quantile, regression functions, and the so-called relative distribution function. In addition, the moment method is applied to the problem of estimating the joint density function of the random coefficients in the linear regression model. Under the assumptions that coefficients of the regression function are non-negative random variables, the new non-parametric density estimator of the unknown density function of coefficients is derived.
Abstract:
As an another example, it is worth mentioning the area of Computed Tomography, where the moment methods are very useful. One can establish the relationship between the moments of observed Radon transform (projections) of f and the moments of original function f (image) itself for recovery of the image f from the values of its Radon transform. We implemented new algorithm to reconstruct f from the values of its Radon transform. Numerical and graphical convergences of our constructions are illustrated by means of tables and graphs.
Bio:
Robert M. Mnatsakanov, PhD, is the Professor of Mathematics at the School of Mathematical and Data Sciences, West Virginia University. He received his PhD in Physics and Mathematics from Moscow Institute of Electronics and Mathematics. Mnatsakanov’s research interests are concentrated in different areas of statistics and mathematics, such as the change-set problem, entropy estimation in multidimensional space, on recovering the distributions in the framework of multidimensional Hausdorff and Stieltjes moment problems, the nonparametric estimation of unknown mixing distributions in Poisson mixture models. He works on reconstructions of unknown intensity functions in Computed Tomography by inverting the Radon and the Laplace transforms using newly developed the moment-recovered approximations.
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- George Mason University
- Fairfax, Virginia
- United States 22030
- Building: Nguyen Engineering Building,
- Room Number: Jajodia Auditorium, Room 1101