2 Minimum distance estimation: The approach using density-based distances

Abstract

This chapter discusses the concept of minimum distance estimation using density-based distances. Density-based minimum distance methods have proven to be valuable additions to the theory of statistics as demonstrated by the rich literature of the past two decades. In parametric models, the estimators often possess full asymptotic efficiency simultaneously with attractive robustness properties. The chapter also discusses minimum Hellinger distance estimation, including the Hellinger deviance test and penalized Hellinger distance estimation. In the chapter, General disparities, residual adjustment functions, and related inference are introduced and the negative exponential disparity and weighted likelihood estimators (including linear regression models) are described. A generalized divergence measure and the resulting estimators are also discussed in the chapter.