Generalized Kramer–Rao inequality for the moments of distribution of estimation error
Abstract
In this paper it's obtained a generalized system of statistical inequalities under additional conditions of regularity of the statistical experiment, which is a generalization of the Cramer–Rao inequality. The resulting system of inequalities allows to find the lower bounds of arbitrary even error moments of estimates of unknown parameters. It's found relations which allow one to approximate and numerically calculate the distribution density of the estimation error with a limited set of cumulant coefficients.
About the Authors
A. V. Ausiannikau
Belarusian state university
Belarus
Belarus
Ausiannikau Andrei Vital'evich - PhD, associate professor of information technologies department
220030, Republic of Belarus, Minsk, Nezavisimosti av., 4
tel. +375-17-209-58-94
V. M. Kozel
Belarusian state university of informatics and radioelectronics
Belarus
PhD, associate professor of information radiotechnologies department
Belarus
PhD, associate professor of information radiotechnologies department
References
1. Ibragimov I.A., Has'minskij R.Z. Asimptoticheskaja teorija ocenivanija. M.: Nauka, 1979. 528 s. (in Russ.)
2. Kramer G. Matematicheskie metody statistiki. M.: Mir, 1975. 648 s. (in Russ.)
3. Ovsjannikov A.V. Statisticheskie neravenstva v sverhreguljarnyh statisticheskih jeksperimentah teorii ocenivanija // Vesti nacyjanal'naj akadjemii navuk Belarusi. Ser fiz-mat. navuk. 2009. № 2. S. 106–110. (in Russ.)
4. Orlov A.I. Sovremennoe sostojanie neparametricheskoj statistiki // Nauchnyj zhurnal KubGAU. 2015. № 106 (02). S. 239–269. (in Russ.)
5. Marshall A., Olkin I. Neravenstva: Teorija mazhorizacii i ejo prilozhenija. M.: Mir, 1983. 576 s. (in Russ.)
6. Cypkin Ja.Z. Informacionnaja teorija identifikacii. M.: Nauka. Fizmatlit, 1995. 336 s. (in Russ.)
7. Ovsjannikov A.V. Robastno-adaptivnyj usilitel'-ogranichitel' // Radiotehnika. 2011. № 3. S. 85–89. (in Russ.)
8. Malahov A.I. Kumuljantnyj analiz sluchajnyh negaussovyh processov i ih preobrazovanij. M.: Sov. radio, 1978. 376 s. (in Russ.)
Review
For citations:
Ausiannikau A.V., Kozel V.M. Generalized Kramer–Rao inequality for the moments of distribution of estimation error. Doklady BGUIR. 2018;(8):42-48. (In Russ.)
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