Local asymptotic normality for shape and periodicity in the drift of a time inhomogeneous diffusion

Simon Holbach ()
Additional contact information
Simon Holbach: Johannes Gutenberg-Universität Mainz

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 3, No 3, 527-538

Abstract: Abstract We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity T and carrying some unknown d-dimensional shape parameter $$\vartheta $$ ϑ . We prove local asymptotic normality (LAN) jointly in $$\vartheta $$ ϑ and T for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $$n^{-1/2}$$ n - 1 / 2 for the shape parameter and $$n^{-3/2}$$ n - 3 / 2 for the periodicity which generalizes known results about LAN when either $$\vartheta $$ ϑ or T is assumed to be known.

Keywords: Local asymptotic normality; Parametric signal estimation; Periodic diffusion; 62F12; 60J60 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11203-017-9157-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:21:y:2018:i:3:d:10.1007_s11203-017-9157-5

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-017-9157-5

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().