Date of Award

Winter 2007

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

N. Rao Chaganty

Committee Member

Dayanand Naik

Committee Member

Larry Lee

Committee Member

Larry Filer

Abstract

Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create and compare various estimators based on existing and emerging methods of estimation. Asymptotic and small-sample properties are discussed, as is hypothesis testing.

The second part of this dissertation involves a slightly more complicated version of autoregressive familial correlation, where we now model heterogeneous intra-class variances. Again we create and compare various estimators and discuss both their asymptotic and small-sample properties.

In the final part of this dissertation we discuss the nuclear family model, basing the familial dependence on an equicorrelated structure. Note that while this correlation structure has been extensively studied in the case of heterogeneous variance, we model homogenous variance and use a new method for estimating the parameters. Noteworthy here is that we apply a linear transformation to simplify both the correlation matrix and the correlation parameter estimators. As before, we generate estimators and compare their asymptotic performance.

DOI

10.25777/zj6m-5347

ISBN

9780549320418

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