Date of Award

6-2013

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Jeffrey T. Terpstra

Second Advisor

Dr. Joseph W. McKean

Third Advisor

Dr. Joshua D. Naranjo

Fourth Advisor

Dr. Donald Kane

Keywords

robust estimate, bifurcating, autoregressive, cell, lineage, weighted, least absolute deviation

Abstract

The bifurcating autoregressive model (BAR) is commonly used to model binary tree data. One application for this model relates to cell lineage data in biology. The purpose of studying the cell lineage process is to know whether the observed correlations between related cells are due to similarities in the environmental, inherited effects, or a combination of both of them. Because outliers in this kind of data are quite common, the need for a robust estimation procedure is necessary. A weighted L1 (WL1) estimate for estimating the parameters of the BAR model is considered. When the weights are constant, the estimate is equivalent to the least absolute deviation estimate (L1). The estimate is shown to be asymptotically normal. Simulated, artificial, and actual examples are presented and it is shown that the unweighted and weighted L1–based estimates are capable of coping with certain kinds of outliers in both response and factor spaces. These estimates, as well as others (e.g. weighted Wilcoxon estimates) are studied via Monte Carlo. Models include both innovation outlier (IO) and additive outlier (AO) models as well as a variety of correlation structures. Overall, most of the estimates perform quite well under a variety of situations. However, no one estimate is superior to the others and the superiority of the estimates depends on the underlying probability model. These findings are consistent with findings in the literature pertaining to autoregressive (AR) time series models.

Access Setting

Dissertation-Open Access

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