Description Usage Arguments Details Value References See Also Examples
Evaluate the coverage probability of the Kabaila & Giri (2009) confidence
interval that utilizes uncertain prior information (CIUUPI),
with minimum coverage 1  alpha
, at gam
.
1  cpciuupi2(gam, bsvec, alpha, m, rho, natural = 1)

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 
alpha 
The minimum coverage probability is 1  
m 
Degrees of freedom 
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

Suppose that
y = X β + ε
where y is a random
nvector of responses, X is a known n by p matrix
with linearly independent columns, β is an unknown parameter
pvector and ε is a random nvector with
components that are independent and identically normally distributed with
zero mean and unknown variance. The parameter of interest is θ =
a
' β. The uncertain prior information is that τ =
c
' β 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 θ and τ. It is determined by the n
by p design matrix X and the pvectors 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
.
The value(s) of the coverage probability of the Kabaila & Giri (2009)
CIUUPI at gam
.
Kabaila, P. and Giri, K. (2009) Confidence intervals in regression utilizing prior information. Journal of Statistical Planning and Inference, 139, 3419  3429.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  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 = 1alpha, lty = 2)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.