rvalues (version 0.7.1)

OverlapCurve: Overlap Curve

Description

Estimates the expected proportion of units in the top fraction and those deemed to be in the top fraction by the r-value procedure. If plot=TRUE, the curve is plotted before the estimated function is returned.

Usage

OverlapCurve(object, plot = TRUE, xlim, ylim, xlab, ylab, main, ...)

Arguments

object

An object of class "rvals"

plot

logical. If TRUE, the estimated overlap curve is plotted.

xlim, ylim

x and y - axis limits for the plot

xlab,ylab

x and y - axis labels

main

the title of the plot

…

additional arguments to plot.default

Value

A function returning estimated overlap values.

Details

For parameters of interest ${\theta }_1,...,{\theta }_n$ and corresponding r-values $r_1,...,r_n$, the overlap at a particular value of $\alpha$ is defined to be $$overlap(\alpha )=P({\theta }_i\ge {\theta }_{\alpha },r_i\le \alpha ),$$ where the threshold ${\theta }_{\alpha }$ is the upper-$\alpha$th quantile of the distribution of the ${\theta }_i$ (i.e., $P({\theta }_i\ge {\theta }_{\alpha })=\alpha$). OverlapCurve estimates this overlap for values of alpha across (0,1) and plots (if plot=TRUE) the resulting curve.

References

Henderson, N.C. and Newton, M.A. (2016). Making the cut: improved ranking and selection for large-scale inference. J. Royal Statist. Soc. B., 78(4), 781-804. 10.1111/rssb.12131 https://arxiv.org/abs/1312.5776

Examples

# NOT RUN {
n <- 500
theta <- rnorm(n)
ses <- sqrt(rgamma(n,shape=1,scale=1))
XX <- theta + ses*rnorm(n)
dd <- cbind(XX,ses)

rvs <- rvalues(dd, family = gaussian)

OverlapCurve(rvs, cex.main = 1.5)
# }