cpciuupi: Compute the coverage probability of the CIUUPI
In ciuupi: Confidence Intervals Utilizing Uncertain Prior Information

Description Usage Arguments Details Value See Also Examples

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

1	cpciuupi(gam, bsvec, alpha, natural = 1, rho = NULL, a, c, x)

`gam`	A value of gamma or vector of gamma values at which the coverage probability function is evaluated
`bsvec`	The vector (b(1),...,b(5),s(0),...,s(5)) that specifies the CIUUPI
`alpha`	The nominal coverage probability is 1 - `alpha`
`natural`	Equal to 1 (default) if the b and s functions are obtained by natural cubic spline interpolation or 0 if obtained by clamped cubic spline interpolation
`rho`	A known correlation
`a`	A vector used to specify the parameter of interest
`c`	A vector used to specify the parameter about which we have uncertain prior information
`x`	The n by p design matrix

Suppose that

y = X β + ε

where y is a random n-vector of responses, X is a known n by p matrix with linearly independent columns, β is an unknown parameter p-vector and ε is the random error with components that are iid normally distributed with zero mean and known variance. The parameter of interest is θ = a' β. The uncertain prior information is that τ = c' β - t = 0, where a and c are specified linearly independent vectors and t is a specified number. rho is the known correlation between the least squares estimators of θ and τ. The user must specify either a, c and x or rho. If a, c and x are specified then rho is computed.

The CIUUPI is specified by the vector (b(1),...,b(5),s(0),...,s(5)), alpha and natural

The value(s) of the coverage probability of the CIUUPI at gam.

ciuupi, bsciuupi

alpha <- 0.05

# Find the vector (b(1),b(2),...,b(5),s(0),s(1),...,s(5)) that specifies the
# CIUUPI: (this may take a few minutes to run)

bsvec <- bsciuupi(alpha, rho = 0.4)


# The result (to 7 decimal places) is
bsvec <- c(0.129443483, 0.218926703, 0.125880945, 0.024672734, -0.001427343,
           1.792489585, 1.893870240, 2.081786492, 2.080407355,  1.986667246,
           1.958594824)

# Graph the coverage probability function
gam <- seq(0, 10, by = 0.1)
cp <- cpciuupi(gam, bsvec, alpha, rho = 0.4)
plot(gam, cp, type = "l", lwd = 2, ylab = "", las = 1, xaxs = "i",
main = "Coverage Probability", col = "blue",
xlab = expression(paste("|", gamma, "|")), ylim = c(0.94999, 0.95001))
abline(h = 1-alpha, lty = 2)