New Control Charts for a Multivariate Gamma Distribution

In this study, a multivariate gamma distribution is first introduced. Then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is based on the normal approximation. Efficiency of the proposed control charts is evaluated by average run length (ARL) criterion.

FastSKAT: Sequence kernel association tests for very large sets of markers

The Sequence Kernel Association Test (SKAT) is widely used to test for associations between a phenotype and a set of genetic variants, that are usually rare. Evaluating tail probabilities or quantiles of the null distribution for SKAT requires computing the eigenvalues of a matrix related to the genotype covariance between markers. Extracting the full set of eigenvalues of this matrix (an n × n matrix, for n subjects) has computational complexity proportional to n3. As SKAT is often used when n > 104, this step becomes a major bottleneck in its use in practice. We therefore propose fastSKAT, a new computationally-inexpensive but accurate approximations to the tail probabilities, in which the k largest eigenvalues of a weighted genotype covariance matrix or the largest singular values of a weighted genotype matrix are extracted, and a single term based on the Satterthwaite approximation is used for the remaining eigenval-ues. While the method is not particularly sensitive to the choice of k, we also describe how to choose its value, and show how fastSKAT can automatically alert users to the rare cases where the choice may affect results. As well as providing faster implementation of SKAT, the new method also enables entirely new applications of SKAT, that were not possible before; we give examples grouping variants by topologically assisted domains, and comparing chromosome-wide association by class of histone marker.