On finite sample statistics for Yule-Walker estimates

Author

Wensink, Einar ; Dijkhof, Wilbert J.

Author_Institution

Thales-Avionics, Valence, France

Volume

49

Issue

2

fYear

2003

Firstpage

509

Lastpage

516

Abstract

The expectation of the square of the reflection coefficient in small samples of white noise is derived. This variance of the reflection coefficient in white noise is a key factor in the statistics of the estimation of autoregressive (AR) models in small samples. Approximations of this expectation are constructed that are more accurate than the known first-order Taylor approximation. These better approximations are needed, because in some applications (radar applications, for example) the number of observations is small (say 63 observations) and asymptotic descriptions do not cover the estimates.

Keywords

autoregressive processes; correlation methods; parameter estimation; polynomial approximation; signal sampling; white noise; AR models; Yule-Walker estimates; autoregressive models; finite sample statistics; parameter estimation; radar applications; real-valued observations; reflection coefficient; small samples; white noise; Acoustic reflection; Differential equations; Least squares approximation; Mathematics; Mechanical engineering; Parameter estimation; Radar applications; Statistics; Thumb; White noise;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.807310

Filename

1176627