Overlap Curve

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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

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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 θ_1,...,θ_n and corresponding r-values r_1,...,r_n, the overlap at a particular value of α is defined to be

overlap(α) = P(θ_i ≥ θ_α, r_i ≤ α),

where the threshold θ_α is the upper-αth quantile of the distribution of the θ_i (i.e., P(θ_i ≥ θ_α) = α). 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. (2015) Making the Cut: Improved Ranking and Selection for Large-Scale Inference. http://arxiv.org/abs/1312.5776

Examples

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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)