fdr.estimate.eta0 estimates the proportion eta0 of null p-values in a given
vector of p-values. This quantity is an important parameter
when controlling the false discovery rate (FDR). A conservative choice is
eta0 = 1 but a choice closer to the true value will increase efficiency
and power
- see Benjamini and Hochberg (1995, 2000) and Storey (2002) for details.
fdr.estimate.eta0(p, method=c("conservative", "adaptive", "bootstrap",
"smoother"), lambda=seq(0,0.95,0.05) )vector of p-values.
algorithm used to estimate the proportion of null p-values. Available options are "conservative" (default), "adaptive", "bootstrap", and "smoother".
optional tuning parameter vector needed for "bootstrap"
and "smoothing" methods (defaults to seq(0,0.95,0.05))
- see Storey (2002) and Storey and Tibshirani (2003).
The estimated proportion eta0 of null p-values.
The function fdr.estimate.eta0 provides four algorithms: the "conservative"
method always returns eta0 = 1 (Benjamini and Hochberg, 1995), "adaptive"
uses the approach suggested in Benjamini and Hochberg (2000), "bootstrap"
employs the method from Storey (2002), and "smoother" uses the smoothing spline
approach in Storey and Tibshirani (2003).
"conservative" procedure: Benjamini, Y., and Y. Hochberg (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. B, 57, 289--300.
"adaptive" procedure: Benjamini, Y., and Y. Hochberg (2000) The adaptive control of the false discovery rate in multiple hypotheses testing with independent statistics. J. Behav. Educ. Statist., 25, 60--83.
"bootstrap" procedure: Storey, J. D. (2002) A direct approach to false discovery rates. J. Roy. Statist. Soc. B., 64, 479--498.
"bootstrap" procedure: Storey, J. D., and R. Tibshirani (2003) Statistical significance for genome-wide experiments. Proc. Nat. Acad. Sci. USA, 100, 9440-9445.