On Bahadur asymptotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes

Yoshihide Kakizawa

Stochastic Processes and their Applications, 2000, vol. 85, issue 1, 29-44

Abstract: In this paper the maximum likelihood and quasi-maximum likelihood estimators of a spectral parameter of a mean zero Gaussian stationary process are shown to be asymptotically efficient in the sense of Bahadur under appropriate conditions. In order to obtain exponential convergence rates of tail probabilities of these estimators, a basic result on large deviation probability of certain quadratic form is proved by using several asymptotic properties of Toeplitz matrices. It turns out that the exponential convergence rates of the MLE and qMLE are identical, which depend on the statistical curvature of Gaussian stationary process.

Keywords: Bahadur; efficiency; Gaussian; stationary; process; Spectral; density; Large; deviation; probability; Quadratic; form; Toeplitz; matrix (search for similar items in EconPapers)
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00063-0
Full text for ScienceDirect subscribers only

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:eee:spapps:v:85:y:2000:i:1:p:29-44

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().