cpciuupi2 {ciuupi2}

Compute the coverage probability of the Kabaila & Giri (2009) CIUUPI

Description

Evaluate the coverage probability of the Kabaila & Giri (2009) confidence interval that utilizes uncertain prior information (CIUUPI), with minimum coverage 1 - alpha, at gam.

Usage

cpciuupi2(gam, bsvec, alpha, m, rho, natural = 1)

Arguments

gam

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

bsvec

The vector (b(d/6),b(2d/6),...,b(5d/6),s(0),s(d/6),...,s(5d/6)) computed using bsciuupi2

alpha

The minimum coverage probability is 1 - alpha

m

Degrees of freedom n - p

rho

A known correlation

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. This parameter must take the same value as that used in bsciuupi2

Details

Suppose that

y = X \beta + \epsilon

where y is a random n-vector of responses, X is a known n by p matrix with linearly independent columns, \beta is an unknown parameter p-vector and \epsilon is a random n-vector with components that are independent and identically normally distributed with zero mean and unknown variance. The parameter of interest is \theta = a' \beta. The uncertain prior information is that \tau = c' \beta takes the value t, 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 \theta and \tau. It is determined by the n by p design matrix X and the p-vectors a and c using find_rho.

In the examples, we continue with the same 2 x 2 factorial example described in the documentation for find_rho.

Value

The value(s) of the coverage probability of the Kabaila & Giri (2009) CIUUPI at gam.

References

Kabaila, P. and Giri, K. (2009) Confidence intervals in regression utilizing prior information. Journal of Statistical Planning and Inference, 139, 3419 - 3429.

See Also

find_rho, bsciuupi2

Examples

alpha <- 0.05
m <- 8

# Find the vector (b(d/6),...,b(5d/6),s(0),...,s(5d/6)) that specifies the
# Kabaila & Giri (2009) CIUUPI for the first definition of the
# scaled expected length (default) (takes about 30 mins to run):

bsvec <- bsciuupi2(alpha, m, rho = -0.7071068)


# The result bsvec is (to 7 decimal places) the following:
bsvec <- c(-0.0287487, -0.2151595, -0.3430403, -0.3125889, -0.0852146,
            1.9795390,  2.0665414,  2.3984471,  2.6460159,  2.6170066,  2.3925494)


# Graph the coverage probability function
gam <- seq(0, 10, by = 0.1)
cp <- cpciuupi2(gam, bsvec, alpha, m, rho = -0.7071068)
plot(gam, cp, type = "l", lwd = 2, ylab = "", las = 1, xaxs = "i",
main = "Coverage Probability", col = "blue",
xlab = expression(paste("|", gamma, "|")), ylim = c(0.9490, 0.9510))
abline(h = 1-alpha, lty = 2)