M-estimation for discrete data: Asymptotic distribution theory and implications. (English) Zbl 0652.62011

Simpson, Douglas G.; Carroll, Raymond J.; Ruppert, David

Ann. Stat. 15, 657-669 (1987).

The authors consider the asymptotic distribution of an M-estimator when the underlying distribution is discrete. They show its asymptotic normality quite generally. When the specification of the model is inexact, however, non-normal limiting distributions may result, and lead the authors to propose smooth score functions for discrete data.

Reviewer: A.N.Philippou

MSC:

62E20	Asymptotic distribution theory in statistics
62F10	Point estimation
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

discrete model; robust estimation; M-estimator; asymptotic normality; non-normal limiting distributions; smooth score functions