OverlapCurve {rvalues}

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

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-\alphath 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.

Value

A function returning estimated overlap values.

Author(s)

Nicholas Henderson and Michael Newton

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. doi: 10.1111/rssb.12131 https://arxiv.org/abs/1312.5776

Examples

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)