## The Annals of Statistics

### Efficient Location and Regression Estimation for Long Range Dependent Regression Models

Rainer Dahlhaus

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 1029-1047.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176324635

Digital Object Identifier
doi:10.1214/aos/1176324635

Mathematical Reviews number (MathSciNet)
MR1345213

Zentralblatt MATH identifier
0838.62084

JSTOR