Variance Estimation in the Additive Tree Model

Abstract

By the use of stochastic models it is possible to judge procedures for fitting additive trees to dissimilarity data. We use the simple additive error model (Degens 1983) to analyse the accuracy of an estimated additive tree by estimating its variance, too. Analogously to the three-object variance estimator in the ultrametric case (cf. Lausen 1987 or Lausen & Degens 1986) we propose a four-object variance estimator based on the simple maximum-likelihood (ML-) variance estimation for all subsets consisting of any four objects of an additive tree. In contrast to variance estimation using the residual sum of squares this new estimator is not based on the assumed i.e. estimated structure of the given dissimilarity data. In the framework of a Monte-Carlo study we analyse the four-object variance estimator and compare it to variance estimators based on linear models in the case of local solutions of the underlying approximation problem (cf. Vach 1988).