# 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

1 |

### 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 |

### 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-*α*th 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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