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

Vajda, I.

Probl. Control Inf. Theory 15, 111-127 (1986).

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

MSC:

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

Keywords:

D-estimator; discrete and continuous families; minimum divergence estimators; minimum chi-square estimators; generalized empirical distribution functions; Influence curves; asymptotic normality; homogeneous Markov chain; location; scale