LBE (version 1.40.0)

LBEa: Optimal setting for the parameter a

Description

The LBEa function is called by the main function LBE for choosing the greatest value of a such that the upper bound of the asymptotic standard deviation is less than a threshold l. A plot illustrating the relation between a and l for a fixed number of tested hypotheses can also be displayed.

Usage

LBEa(m, l = 0.05, fig = TRUE, a.rng = NA)

Arguments

m

Total number of tested hypotheses.

l

Threshold for the upper bound of the asymptotic standard deviation (default value is 0.05).

fig

Logical value for plotting the standard deviation versus a.

a.rng

Range of values of a to consider. If a.rng == NA, a.rng is set such that the standard deviation is less than 0.5.

Value

• a
  Greatest value of a such that the the upper bound of the asymptotic standard deviation of the estimator of pi0 is smaller than the threshold l.

Details

The procedure LBE is based on the expectation of a particular transformation of the p-values leading to a straightforward estimation of the key quantity pi0 that is the proportion of true null hypotheses: $$pi0(a)={(1/m)*\sum_{i=1}^{m}[-\ln(1-pi)]^a]}/\Gamma(a+1)$$ where a belongs to the interval $[1;inf)$. As there is a balance between bias (decreasing as a increase) and variance (increasing as a increase), for a specified number m of tested hypotheses, we have proposed to choose the greatest value of a such that the upper bound of the asymptotic standard deviation of the estimator of pi0 is smaller than the threshold l. The function LBEa allows to plot the standard deviation versus a in order to help for the choice of the threshold l (for a specific number m of tested hypotheses).

References

Dalmasso C, Broet P, Moreau T (2005). A simple procedure for estimating the false discovery rate. Bioinformatics. Bioinformatics, 21: 660 - 668.

See Also

LBE, LBEplot, LBEsummary, LBEwrite

Examples

## start
data(hedenfalk.pval)
m <- length(hedenfalk.pval)
LBEa(m,l = 0.05)
## end