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Robust inference for variance components models for single trees of cell lineage data. (English) Zbl 0865.62016
Summary: R. M. Huggins and R. G. Staudte [J. Am. Stat. Assoc. 89, No. 425, 19-29 (1994)] 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.

MSC:
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J10 Analysis of variance and covariance (ANOVA)
62M99 Inference from stochastic processes
60G09 Exchangeability for stochastic processes
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