Estimating FDP Under Arbitrary Covariance Dependence Based On Best Linear Unbiased Prediction

Multiple hypothesis testing is a fundamental problem in high-dimensional statistical inference with wide applications in many scientific fields. Especially,in genomewide association studies,tens of thousands of tests are tested simultaneously, in order to find the single-nucleotide polymorphisms related with some diseases.When conducting multiple hypothesis testing, it is extremely important to control the overall error rates. To solve this problem, Benjamini and Hochberg(1995)[1]put forward to the false discovery rate.Benjamini and Yekutieli(2001)[2],Efron(2007)[3]have did in-depth discussions to the FDR.However they were as a prerequisite to supposing the null hypothesis independently with each other.But as we know,this assumption is not realistic.Because in practical problems the test statistics are often correlated with each other.Based on this situation, Jianqing Fan(2012)[5]put forward to a method of controlling false discovery proportion under arbitrary covariance dependence.In the article,he applied eigen-decomposition to the covariance matrix,resulting in a model= + bW + , = 1, · · ·, . When he estimated W,he used 1estimation method regarding it as a parameter.In this paper, when we control FDP under arbitrary covariance dependence,we consider the above model as a mixed model,that is,we regard W as a random variable.Finally,we obtain a new FDP estimating.Simulation shows that FDP in our method varies around true values, which is more reasonable.