## Analysis of transformations of linear random-effects models

Assume that a linear random-effects model (LRM) \$\by = \bX \bbe + \bve = \bX\bbe+ \bve\$ with \$\bbe = \bA \bal + \bga\$ is transformed as \$\bT\by = \bT\bX\bbe + \bT\bve = \bT\bX\bA \bal + \bT\bX\bga + \bT\bve\$ by pre-multiplying a given matrix \$\bT\$. Estimations/predictions of the unknown parameters under the two models are not … Read more

## A new algebraic analysis to linear mixed models

This article presents a new investigation to the linear mixed model \$\by = \bX \bbe + \bZ\bga + \bve\$ with fixed effect \$\bX\bbe\$ and random effect \$\bZ\bga\$ under a general assumption via some novel algebraic tools in matrix theory, and reveals a variety of deep and profound properties hidden behind the linear mixed model. We … Read more

## Calibrating Least Squares Covariance Matrix Problems with Equality and Inequality Constraints

In many applications in statistics, finance, and insurance/reinsurance, one seeks a solution of finding a covariance matrix satisfying a large number of given linear equality and inequality constraints in a way that it deviates the least from a given symmetric matrix. The difficulty in finding an efficient method for solving this problem is due to … Read more