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Theses/Dissertations

Statistics and Probability

2006

Mathematics & Statistics Theses & Dissertations

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Full-Text Articles in Physical Sciences and Mathematics

Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng Jul 2006

Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng

Mathematics & Statistics Theses & Dissertations

Analysis of dependent continuous and discrete data has become an active area of research. For normal data, correlations fully quantify the dependence. And historically, maximum likelihood method has been very successful to estimate the correlations and unbiased estimating equation approach has become a popular alternative when there may be a departure from normality. In this thesis we show that the optimal unbiased estimating equation coincides with the likelihood equations for normal data. We then introduce a general class of weighted unbiased estimating equations to estimate parameters in a structured correlation matrix. We derive expressions for asymptotic covariance of the estimates, …


Estimating Familial Correlations Using A Kotz Type Density, Amal Helu Jul 2006

Estimating Familial Correlations Using A Kotz Type Density, Amal Helu

Mathematics & Statistics Theses & Dissertations

Two useful familial correlations often used to study the resemblance between the family members are the sib-sib correlation (ρss) and the mom-sib or parent-sib correlation (ρps). Since their introduction early in the last century by Galton, Fisher and others, many improved estimators of these correlations have been suggested in the literature. Several moment based estimators as well as the maximum likelihood estimators under the assumption of multivariate normality have been extensively studied and compared by various authors. However, the performance of these estimators when the data are not from multivariate normal distribution is poor. In this …