A0823
Title: An algorithm for searching optimal variance component estimators in linear mixed models
Authors: Subir Ghosh - University of California (United States) [presenting]
Abstract: An algorithm is developed to derive strictly positive unbiased estimators with minimum variance in a well-defined class. The key idea is to take the method-of-moments estimator, given by a quadratic form of a symmetric matrix $A$, as a starting point and modify it using the class of square non-singular regularization matrices $Q$ while preserving unbiasedness in addition to ensuring positivity. Different subclasses of structured $Q$ are possible for convenience instead of all possible $Q$ matrices. A search algorithm then finds a local or global optimal matrix $A$ depending on $Q$ and the corresponding optimal variance component estimator by minimizing the variance, a function of the unknown variance components and kurtosis parameters. The proposed method further allows finding matrices $A$ leading to quadratic forms closely approximating the corresponding numerical values of the likelihood-based estimates. In addition, the dependence of variance functions is investigated on unknown model parameters. Using two illustrative examples, Examples I and II, the report also illustrates the use of the matrix $Q$ and the determination of the kurtosis parameters in the search for the optimal variance component estimators by keeping the bias zero and the variance trim for the bias-variance trade-offs.
