cpciuupi {ciuupi}

Compute the coverage probability of the CIUUPI

Description

Evaluate the coverage probability of the confidence interval that utilizes uncertain prior information (CIUUPI) at gam. 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

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

Arguments

gam

A value of \gamma or vector of values of \gamma 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 coverage probability

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 coverage probability of the CIUUPI at gam.

Examples

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