Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions

Yuri S. Popkov
Additional contact information
Yuri S. Popkov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2021, vol. 9, issue 5, 1-13

Abstract: The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

Keywords: randomized maximum entropy estimation; probability density functions; Lagrange multipliers; Lyapunov-type problems; implicit function; rotation of vector field; asymptotic efficiency; thermokarst lakes; forecasting (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/5/548/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/5/548/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:5:p:548-:d:510995

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().