mutoss (version 0.1-3)

BR_pi0_est: Estimate of pi0 using the one-step Blanchard-Roquain procedure

Description

The proportion of true nulls is estimated using the Blanchard-Roquain 1-stage procedure with parameter (alpha,lambda) via the formula

Usage

BR_pi0_est(pValues, alpha, lambda=1, truncate=TRUE)

Arguments

pValues

The raw p-values for the marginal test problems (assumed to be independent)

alpha

The FDR significance level for the BR procedure

lambda

(default 1) The parameter for the BR procedure, shoud belong to (0, 1/alpha)

truncate

(logical, default TRUE) if TRUE, output estimated is truncated to 1

Value

• pi0
  The estimated proportion of true null hypotheses.

Details

estimated pi_0 = ( m - R(alpha,lambda) + 1) / ( m*( 1 - lambda * alpha ) )

where R(alpha,lambda) is the number of hypotheses rejected by the BR 1-stage procedure, alpha is the FDR level for this procedure and lambda a parameter belonging to (0, 1/alpha) with default value 1. Independence of p-values is assumed. This estimate may in some cases be larger than 1; it is truncated to 1 if the parameter truncated=TRUE. The estimate is used in the Blanchard-Roquain 2-stage step-up (using the non-truncated version)

References

Blanchard