exactCoverageProb: Evaluate exact coverage probability

In popKorn: For interval estimation of mean of selected populations

Description

This function will evaluate the exact coverage probability, as given in equation (4) on page 7 of the paper. See Details section.

Usage

exactCoverageProb(c.vec, theta.diff, lambda, c.val, sigma.2 = 1, n = 1)

Arguments

c.vec	This is a vector of length 2. It consists of the lower and upper limits in the integral. Checking is carried out to ensure that is of length two, and that 0 <= c.vec[1] <= c.vec[2]. This parameter is ignored if lambda is not missing.
theta.diff	A vector of length p-1, where p is the number of populations of treatments. Coordinate [i] in theta.diff corresponds to θ_i - θ_{i+1}. See genDelMat.
lambda	In case the user wishes to use the shrinkage version, this parameter should be specified. It must be between 0 and 1.
c.val	In case lambda is specified, this must not be missing. This will be combined with lambda to create a c.vec. This very function will then call itself.
sigma.2	The known variance of the error terms.
n	The number of replications per population.

Details

This function evaluates the coverage probability for an interval defined by (X_{(1)} - c_2, X_{(1)} + c_1). Note that, as specified in the reference paper, we must have that 0 ≤ c_1 ≤ c_2. This function will call integrate2. Please note the ordering of the elements in the c.vec argument: the first element corresponds to the upper limit of the interval, and to the negative of the lower limit of the integral.

Value

The function returns a scalar value that is the value of the exact coverage coverage probability defined in equation (4) of page 7.

See Also

integrate2, integrand

Examples

del1 <- c(2, 4)
exactCoverageProb(c(1.1,1.3), del1)
exactCoverageProb(theta.diff=c(2,3,4), lambda=0.9, c.val=2)

popKorn documentation built on May 2, 2019, 8:31 a.m.