An estimating fonction for a scalar parameter in a covariance operator

Christian Lavergne (1) , Anestis Antoniadis (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

Presented here are results about an estimating function for producing estimates of a scalar parameter contained multiplicatively in the covariance operator of a strongly second order $m$-dimensional random vector (r.v.). We study the asymptotic properties of estimates obtained when observing $n$ independent and identically distributed r.v.'s on the model. Under modest assumptions, the consistency and the asymptotic normality of the obtained sequences of estimates are ascertained. The theory is illustrated by an example from reliability and our estimates are compared to maximum likelihood variance components estimates via simulations.

Mots clés: least squares; estimating function; efficacy; variance components; optimal estimators

Domaines: Statistiques [math.ST]

Christian Lavergne, Anestis Antoniadis. An estimating fonction for a scalar parameter in a covariance operator. Statistics and Decisions, 1994, 12 (1), pp.53-65. ⟨10.1524/strm.1994.12.1.53⟩. ⟨hal-00196121⟩