On least absolute deviation estimators for one-dimensional chirp model

Abstract

It is well known that the least absolute deviation (LAD) estimators are more robust than the least squares estimators particularly in presence of heavy tail errors. We consider the LAD estimators of the unknown parameters of one-dimensional chirp signal model under independent and identically distributed error structure. The proposed estimators are strongly consistent and it is observed that the asymptotic distribution of the LAD estimators are normally distributed. We perform some simulation studies to verify the asymptotic theory for small sample sizes and the performance are quite satisfactory.

Keywords:

• chirp signals
• least absolute deviation estimators
• strong consistency
• asymptotic distribution

Acknowledgements

The work of the first author has been financially supported by the Center for Scientific and Industrial Research (CSIR), and the work of the second and third authors have been partially financially supported by a grant from the Department of Science and Technology, Government of India. The authors thank the referees for their constructive comments, which had helped to improve the earlier version of the manuscript.