Semiparametric Regression of Multidimensional Genetic Pathway Data: Least‐Squares Kernel Machines and Linear Mixed Models

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Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control (2011, background): “Unlike classical tests, this test does not degenerate when the number of model parameters under the alternative exceeds the sample size, making the test useful for applications in genetics and genomics (Goeman et al., 2004; Liu et al., 2007; Pan, 2009).”
Optimal tests for rare variant effects in sequencing association studies. (2012, methodology): “For a fixed ρ, Qρ follows a mixture of chi-square distributions [17, 8, 7].”
Rare-variant association testing for sequencing data with the sequence kernel association test. (2011, methodology): “Estimating the Null Distribution for Q Under the null hypothesis, Q follows a mixture of chisquare distributions.(29,30) More specifically, we define P0 1⁄4 V V ~ Xð ~ XV ~ XÞ 1 ~ XV where ~ X is the n 3 (p þ 1) matrix equal to [1, X].”