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June, 1995 Efficient Location and Regression Estimation for Long Range Dependent Regression Models
Rainer Dahlhaus
Ann. Statist. 23(3): 1029-1047 (June, 1995). DOI: 10.1214/aos/1176324635


In this paper we construct an efficient weighted least squares estimator for the mean and more generally for the regression parameters in certain Gaussian long range dependent regression models, including polynomial regression. The form of the estimator does not depend on the whole dependence structure of the residuals, but only on the local behaviour of the spectral density at zero. By using an estimator of the self-similarity parameter, we give a fully efficient estimator. Furthermore, we construct efficient weighted $M$-estimators.


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Rainer Dahlhaus. "Efficient Location and Regression Estimation for Long Range Dependent Regression Models." Ann. Statist. 23 (3) 1029 - 1047, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0838.62084
MathSciNet: MR1345213
Digital Object Identifier: 10.1214/aos/1176324635

Primary: 62F12
Secondary: 60F99 , 62M10

Keywords: $M$-estimates , efficiency , Long range dependence , weighted least squares estimates

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
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