Robust estimation in discrete and continuous families by means of a minimum chi-square method. (English) Zbl 0609.62053

Author’s summary: Sharper variants of former results concerning minimum divergence estimators are presented. The class of minimum chi-square estimators, which can be defined as \(L_ 2\)-projections of generalized empirical distribution functions into families of generalized theoretical distribution functions is studied in more detail. Influence curves are evaluated and asymptotic normality is established. Examples concerning parameters of a homogeneous Markov chain and concerning parameters of location and scale are presented.
Reviewer: E.P.Gilbo


62F35 Robustness and adaptive procedures (parametric inference)
62F10 Point estimation
62G30 Order statistics; empirical distribution functions