Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes

Didier A. Girard

Statistics & Probability Letters, 2016, vol. 110, issue C, 191-197

Abstract: Consider one realization of a continuous-time Gaussian process Z which belongs to the Matérn family with known regularity index ν>0. For estimating the autocorrelation-range and the variance of Z from n observations on a fine grid, we propose two simple estimating functions based on the “candidate Gibbs energy” (GE) and the empirical variance (EV). Here a candidate GE designates the quadratic form zTR−1z/n where z is the vector of observations and R is the autocorrelation matrix for z associated with a candidate range. We show that the ratio of the large-n mean squared error of the resulting GE–EV estimate of the range-parameter to the one of its maximum likelihood estimate, and the analog ratio for the variance-parameter, both converge, when the grid-step tends to 0, toward a constant, only function of ν, surprisingly close to 1 provided ν is not too large. This latter condition on ν has not to be imposed to obtain the convergence to 1 of the analog ratio for the microergodic-parameter. Possible extensions of this approach, which could be rather easily implemented, are briefly discussed.

Keywords: ARMA; Gaussian process; Maximum likelihood; Estimating functions; Matérn autocorrelation (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715215302935
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:stapro:v:110:y:2016:i:c:p:191-197

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

DOI: 10.1016/j.spl.2015.12.021

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().