A Consistent Estimator for Linear Models with Dependent Observations

Abstract

In this article, an estimator for the classical linear model and its generalization for the linear measurement error model are studied in the case of dependent (strong mixing) observations. These estimators are based on the Fourier transform of a certain weight function. Consistency of both estimators is established and asymptotic normality is proved for the estimator in the classical model. Simulation results are also presented for both models.

Key Words:

• Linear model
• Measurement error
• Strong mixing
• Consistency
• Asymptotic normality
• Fourier transform

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62F12

Acknowledgments

The author wants to thank István Fazekas for helpful discussions about this topic and for his suggestions and useful remarks. This research is supported by the Hungarian National Science Foundation OTKA under Grant No. F 032060/2000 and by the Bolyai Grant of the Hungarian Academy of Sciences.