ROBUST METHODS FOR DEPENDENT CELL PEDIGREE DATA

This paper studies a robust approach to the analysis of cell pedigree data, building on the work of Huggins & Marschner (1991) which discussed M-estimation for the so-called bifurcating autoregressive process. The study allows for incomplete observation of the pedigree, and incorporates the possibility of additive effects outliers, as discussed in the time series literature. Some properties of the proposed estimation procedure are studied, including a Monte Carlo investigation of robustness in the presence of contamination.     

Estimation for a first-order bifurcating autoregressive process with heavy-tail innovations

Asymptotics of an alternative extreme-value estimator for the autocorrelation parameter in a first-order bifurcating autoregressive (BAR) process with non-gaussian innovations are derived. This contrasts with traditional estimators whose asymptotic behavior depends on the central part of the innovation distribution. Within any BAR model, the main concern is addressing the complex dependency between generations. The inability of traditional methods to handle this dependency motivated an alternative procedure. With the combination of an extreme-value approach and a clever blocking argument, the dependency issue within the BAR process was resolved, which in turn allowed us to derive the limiting distribution for the proposed estimator through the use of regular variation and non-stationary point processes. Finally, the implications of our extreme-value approach are discussed with an extensive simulation study that not only assesses the reliability of our proposed estimate but also presents the findings for a new estimator of an unknown location parameter θ and its implications.     

Weighted L1-estimates for the First-order Bifurcating Autoregressive Model

We developed robust estimators that minimize a weighted L₁ norm for the first-order bifurcating autoregressive model. When all of the weights are fixed, our estimate is an L₁ estimate that is robust against outlying points in the response space and more efficient than the least squares estimate for heavy-tailed error distributions. When the weights are random and depend on the points in the factor space, the weighted L₁ estimate is robust against outlying points in the factor space. Simulated and artificial examples are presented. The behavior of the proposed estimate is modeled through a Monte Carlo study.     

ROBUST ANALYSIS OF THE BIFURCATING AUTOREGRESSIVE MODEL IN CELL LINEAGE STUDIES

A robust estimation procedure for the bifurcating autoregressive model in cell lineage studies is proposed. The method is illustrated by application to a real data set and is compared with least squares estimates in a small simulation study.