Robust inference for variance components models for single trees of cell lineage data

Abstract

Previously, Huggins and Staudte examined robust estimators for a variance components formulation of the bifurcating autoregressive model for cell lineage data. They gave asymptotic properties of the estimators if a large number of trees were observed. However, for single trees the derivation of these asymptotic properties is more complex. Here the asymptotic distributions of robust estimators of parameters associated with the stationary bifurcating autoregressive process as a single tree becomes large are obtained. These results follow from the formulation of the estimating functions as the product of a nonrandom matrix and the sum of vectors of functions of an infinite sequence of exchangeable random variables.