Pitman estimators: An asymptotic variance revisited

Novikov, A; Kordzakhia, N

Pitman estimators: An asymptotic variance revisited

Novikov, A

Kordzakhia, N

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Publication Type:: Journal Article
Citation:: Theory of Probability and its Applications, 2013, 57 (3), pp. 521 - 529
Issue Date:: 2013-09-19

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Field	Value	Language
dc.contributor.author	Novikov, A https://orcid.org/0000-0001-8529-173X	en_US
dc.contributor.author	Kordzakhia, N	en_US
dc.date.issued	2013-09-19	en_US
dc.identifier.citation	Theory of Probability and its Applications, 2013, 57 (3), pp. 521 - 529	en_US
dc.identifier.issn	0040-585X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/26436
dc.description.abstract	We provide an analytic expression for the variance of ratio of integral functionals of fractional Brownian motion which arises as an asymptotic variance of Pitman estimators for a location parameter of independent identically distributed observations. The expression is obtained in terms of derivatives of a logarithmic moment of the integral functional of limit likelihood ratio process (LLRP). In the particular case when the LLRP is a geometric Brownian motion, we show that the established expression leads to the known representation of the asymptotic variance of Pitman estimator in terms of Riemann zeta-function. © by SIAM.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP120102398
dc.relation.ispartof	Theory of Probability and its Applications	en_US
dc.relation.isbasedon	10.1137/S0040585X9798614X	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Pitman estimators: An asymptotic variance revisited	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	57	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	57	en_US

Abstract:

We provide an analytic expression for the variance of ratio of integral functionals of fractional Brownian motion which arises as an asymptotic variance of Pitman estimators for a location parameter of independent identically distributed observations. The expression is obtained in terms of derivatives of a logarithmic moment of the integral functional of limit likelihood ratio process (LLRP). In the particular case when the LLRP is a geometric Brownian motion, we show that the established expression leads to the known representation of the asymptotic variance of Pitman estimator in terms of Riemann zeta-function. © by SIAM.

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http://hdl.handle.net/10453/26436