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Probability Vector Estimation under Constraints by Discounting

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Wirsching, Günther ; Fischer, Hans:
Probability Vector Estimation under Constraints by Discounting.
Eichstätt : Katholische Universität Eichstätt-Ingolstadt, Mathematisch-Geographische Fakultät, 2011. - 26 S. - (Preprint-Reihe Mathematik ; 2011-4)

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Verfügbar unter folgender Lizenz: Creative Commons BY-NC-SA: Namensnennung, nicht kommerziell, Weitergabe unter gleichen Bedingungen.

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Kurzfassung/Abstract

The focus of this paper is on using observations to estimate an unknown probability vector p = (p1,...,pN) supposed to underlie a multinomial process. In some technical applications, e.g., parameter estimation for a hidden Markov chain, numerical stability can be guaranteed only if we assume each estimate for a probability conforming to the constraint of being always above a positive threshold depending on the particular technical application. Aiming at such estimates we present a fast discounting algorithm which comprises ad-hoc methods known as absolute discounting, linear discounting, and square-root discounting as special cases. In order to base discounting on probabilistic principles, we adopt a Bayesian approach, and we show that, presupposing an arbitrary nonvanishing prior, minimizing the maximum-norm of a certain risk vector defined by a one-sided loss function leads to a new consistent estimator.
It turns out to be quite natural to derive from this an (in general inconsistent) estimator meeting the above described constraints. Using asymptotic statistics, we show that a good approximation to this estimator can be reached by means of our fast discounting algorithm in context with an appropriate adjustment of square-root discounting.

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Publikationsform:Preprint, Working paper, Diskussionspapier
Schlagwörter:Discounting; one-sided risk; Bayesian parameter estimation; asymptotic methods; Markov chain parameter estimation
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Algebra (bis 2009)
Mathematisch-Geographische Fakultät > Mathematik > Didaktik der Mathematik
Titel an der KU entstanden:Ja
Eingestellt am:04. Mai 2011 08:52
Letzte Änderung:17. Jul 2012 15:52
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/6889/