PC Adjusted Testing for Low Dimensional Parameters

In this paper we consider the effect of high dimensional Principal Component (PC) adjustments while inferring the effects of variables on outcomes. This problem is particularly motivated by applications in genetic association studies where one performs PC adjustment to account for population stratification. We consider simple statistical models to obtain asymptotically precise understanding of when such PC adjustments are supposed to work in terms of providing valid tests with controlled Type I errors. We also verify these results through a class of numerical experiments