# Two-step estimation method of Benjamini, Krieger and Yekutieli for estimating pi0

### Description

The two-step estimation method of Benjamini, Krieger and Yekutieli for estimating pi0 is applied to pValues. It consists of the following two steps: Step 1. Use the linear step-up procedure at level alpha' =alpha/(1+alpha). Let r1 be the number of rejected hypotheses. If r1=0 do not reject any hypothesis and stop; if r1=m reject all m hypotheses and stop; otherwise continue. Step 2. Let \hat{m0} =(m - r1) and \hat{pi0} = \hat{m0} / m.

### Usage

 1 TSBKY_pi0_est(pValues, alpha) 

### Arguments

 pValues The raw p-values for the marginal test problems alpha The parameter (to be interpreted as significance level) for the procedure

### Value

 pi0.TSBKY The estimated proportion of true null hypotheses.

WerftWiebke

### References

Benjamini, Y., Krieger, A. and Yekutieli, D. (2006). Adaptive linear step-up procedures that control the false discovery rate Biometrika 93, 3, page 495.

### Examples

 1 2 my.pvals <- c(runif(50), runif(50, 0, 0.01)) result <- TSBKY_pi0_est(my.pvals, 0.1) 

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