selciuupi {ciuupi}

Compute the scaled expected length of the CIUUPI

Description

Evaluate the scaled expected length of the confidence interval that utilizes uncertain prior information (CIUUPI) at gam. This scaled expected length is defined to be the expected length of the CIUUPI divided by the expected length of the standard 1 - \alpha confidence interval. The input bs.list determines the functions b and s that specify the confidence interval that utilizes the uncertain prior information (CIUUPI), for all possible values of \sigma and observed response vector.

Usage

selciuupi(gam, n.nodes, bs.list)

Arguments

gam

A value of \gamma or vector of \gamma values at which the coverage probability function is evaluated

n.nodes

The number of nodes for the Gauss Legendre quadrature used for the evaluation of the scaled expected length

bs.list

A list that includes the following components.

alpha: 1 - \alpha is the desired minimum coverage probability of the confidence interval

rho: The known correlation \rho between \widehat{\theta} and \widehat{\tau}

natural: 1 when the functions b and s are specified by natural cubic spline interpolation or 0 if these functions are specified by clamped cubic spline interpolation

d: the functions b and s are specified by cubic splines on the interval [-d, d]

n.ints: number of equal-length intervals in [0, d], where the endpoints of these intervals specify the knots, belonging to [0, d], of the cubic spline interpolations that specify the functions b and s. In the description of bsvec, n.ints is also called q.

bsvec: the (2q-1)-vector

\big(b(h),...,b((q-1)h), s(0),s(h)...,s((q-1)h)\big),

where q=ceiling(d/0.75) and h=d/q.

Value

The value(s) of the scaled expected length at gam.

Examples

gam <- seq(0, 10, by = 0.2)
n.nodes <- 10
sel <- selciuupi(gam, n.nodes, bs.list.example)