# Changes

## RAREMETAL METHOD

, 23:55, 8 April 2014
SKAT META ANALYSIS
$\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}$,
where $\mathbf{W}$ is the a diagonal matrix of weights of rare variants included in a gene.
As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059 '''Wu et. al'''], the null distribution of the $\mathbf{Q}$ statistic follows a mixture chi-sqaured distribution described as
$\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2},$ where $\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)$ are eigen values of $\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}$.
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