In this paper the detection of rare variants association with continuous phenotypes of interest
is investigated via the likelihood-ratio based variance component test under the framework of linear
mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance
component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare
distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation
of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement.
Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to
evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the
identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective
approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.
Keywords: Rare variants association study, Variance component, Likelihood ratio test, Linear mixed model, Bootstrap test,
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