Abstract

Minimum disparity estimation is appealing in that the estimates it provides are simultaneously robust and efficient. This paper presents a family of algorithms called iteratively reweighted least integrated squares for minimum disparity computation. This family of algorithms, indexed by a real parameter α, approximates the disparity measure by quadratic functions, in a form of integrated weighted squared errors, and minimizes the quadratic functions conveniently by using weighted least squares linear regression algorithms. Among all potential values of α, we advocate the use of α=1 from the consideration of robust estimation, which results in an algorithm similar in spirit to the Fisher scoring method for maximum likelihood computation. Numerical studies show that the new algorithms, especially the one that uses α=1, give competitive or better performance over the other algorithms available in the literature.

Keywords: Disparity; Hellinger distance; Robust estimation; Quadratic programming; Iteratively reweighted least squares; Newton-like methods

Article Outline

1. Introduction

2. Minimum disparity estimation

3. Iteratively reweighted least integrated squares

4. The Cressie–Read family

5. Numerical studies

5.1. Contaminated normals

5.2. Contaminated t distributions

5.3. Mixtures of normals

6. Summary and remarks

Acknowledgements

References