A Jackknife Method for Estimation of Variance Components

Abstract

This paper concerns a method of estimation of variance components in a random effect linear model. It is mainly a resampling method and relies on the Jackknife principle. The derived estimators are presented as least squares estimators in an appropriate linear model, and one of them appears as a MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimator. Our resampling method is illustrated by an example given by C. R. Rao [7] and some optimal properties of our estimator are derived for this example. In the last part, this method is used to derive an estimation of variance components in a random effect linear model when one of the components is assumed to be known.

Keywords:

• AMS classification
• Primary 62J05
• 62F10
• secondary 62G09

Keywords:

• random effect linear models
• Jackknife estimators
• MINQUE