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Theory of Probability and Mathematical Statistics

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Parameter estimation for reciprocal gamma Ornstein-Uhlenbeck type processes


Authors: N. Leonenko, L. Sakhno and N. Šuvak
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 137-154
MSC (2010): Primary 60G10, 60J60, 62M05, 62M15
DOI: https://doi.org/10.1090/S0094-9000-2013-00894-1
Published electronically: August 20, 2013
MathSciNet review: 2986455
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider parameter estimation for a process of Ornstein-Uhlenbeck type with reciprocal gamma marginal distribution, to be called reciprocal gamma Ornstein-Uhlenbeck (RGOU) process. We derive minimum contrast estimators of unknown parameters based on both the discrete and the continuous observations from the process as well as moments based estimators based on discrete observations. We prove that proposed estimators are consistent and asymptotically normal. The explicit forms of the asymptotic covariance matrices are determined by using the higher order spectral densities and cumulants of the RGOU process.


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Additional Information

N. Leonenko
Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF244AG, UK
Email: LeonenkoN@Cardiff.ac.uk

L. Sakhno
Affiliation: Department of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, 64, Volodymyrs’ka St., 01601 Kyiv, Ukraine
Email: lms@univ.kiev.ua

N. Šuvak
Affiliation: Department of Mathematics, University of Osijek, Gajev Trg 6, HR-31 000 Osijek, Croatia
Email: nsuvak@mathos.hr

DOI: https://doi.org/10.1090/S0094-9000-2013-00894-1
Keywords: Ornstein--Uhlenbeck type process, reciprocal gamma distribution, infinite divisibility, self-decomposability, parameter estimation, method of moments, minimum contrast method, Ibragimov functionals, Whittle functionals
Published electronically: August 20, 2013
Additional Notes: Partly supported by the Commission of the European Communities grant PIRSES-GA-2008-230804 within the programme ‘Marie Curie Actions’ and the grant of the United Kingdom Association of Alumni and Friends of Croatian Universities (AMAC-UK)
Article copyright: © Copyright 2013 American Mathematical Society

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