Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng
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
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 …