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Bias-correction of the maximum likelihood estimator for the α-Brownian bridge
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2014 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 93, 78-86 p.Article in journal (Refereed) Published
Abstract [en]

The bias of the maximum likelihood estimator of the parameter α in the α-Brownian bridge is derived. A bias-correction which improves the estimator substantially is proposed. The corrected estimator and Bayesian estimators are compared in a simulation study.

Place, publisher, year, edition, pages
2014. Vol. 93, 78-86 p.
Keyword [en]
α-Brownian bridge, Bias-correction, Estimation, Scaled Brownian bridge
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-229177DOI: 10.1016/j.spl.2014.06.020ISI: 000341479500012OAI: oai:DiVA.org:uu-229177DiVA: diva2:736005
Note

Title also written as: Bias-correction of the maximum likelihood estimator for the alpha-Brownian bridge

Available from: 2014-08-04 Created: 2014-08-04 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Gaussian Bridges: Modeling and Inference
Open this publication in new window or tab >>Gaussian Bridges: Modeling and Inference
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of a summary and five papers, dealing with the modeling of Gaussian bridges and membranes and inference for the α-Brownian bridge.

In Paper I we study continuous Gaussian processes conditioned that certain functionals of their sample paths vanish. We deduce anticipative and non-anticipative representations for them. Generalizations to Gaussian random variables with values in separable Banach spaces are discussed. In Paper II we present a unified approach to the construction of generalized Gaussian random fields. Then we show how to extract different Gaussian processes, such as fractional Brownian motion, Gaussian bridges and their generalizations, and Gaussian membranes from them.

In Paper III we study a simple decision problem on the scaling parameter in α-Brownian bridges. We generalize the Karhunen-Loève theorem and obtain the distribution of the involved likelihood ratio based on Karhunen-Loève expansions and Smirnov's formula. The presented approach is applied to a simple decision problem for Ornstein-Uhlenbeck processes as well. In Paper IV we calculate the bias of the maximum likelihood estimator for the scaling parameter and propose a bias-corrected estimator. We compare it with the maximum likelihood estimator and two alternative Bayesian estimators in a simulation study. In Paper V we solve an optimal stopping problem for the α-Brownian bridge. In particular, the limiting behavior as α tends to zero is discussed.

Place, publisher, year, edition, pages
Uppsala: Uppsala University, Department of Mathematics, 2014. 32 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 86
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:uu:diva-232544 (URN)978-91-506-2420-5 (ISBN)
Public defence
2014-11-07, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2014-10-17 Created: 2014-09-19 Last updated: 2014-10-30Bibliographically approved

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Görgens, MaikThulin, Måns

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