| bs.list.example {ciuupi} | R Documentation |
The list that specifies the CIUUPI for the example
Description
In this example, the dataset described in Table 7.5 of Box et al. (1963) is used.
The design matrix X is
specified by the command
X <- cbind(rep(1,4), c(-1, 1, -1, 1), c(-1, -1, 1, 1), c(1, -1, -1, 1)).
A description of the parameter of interest is given in Discussion 5.8, p.3426 of
Kabaila and Giri (2009).
The parameter of interest is \theta = a^{\top} \beta,
where the column vector a is specified by the command
a <- c(0, 2, 0, -2).
For this example, we have uncertain prior information that
\tau = c^{\top} \beta = 0, where the column vector c is specified by the command
c <- c(0, 0, 0, 1).
The known correlation \rho between \widehat{\theta} and \widehat{\tau} is
computed using the command
rho <- acX_to_rho(a, c, X).
The desired minimum coverage probability of the CIUUPI is 1 - \alpha, where
\alpha = 0.05, which is specified by the command
alpha <- 0.05.
The CIUUPI is determined by \alpha and \rho and is found using the
command
bs.list.example <- bs_ciuupi(alpha, rho),
which takes about 5 minutes to run.
Usage
bs.list.example
Format
An object of class list of length 8.
References
Box, G.E.P., Connor, L.R., Cousins, W.R., Davies, O.L., Hinsworth, F.R., Sillitto, G.P. (1963) The Design and Analysis of Industrial Experiments, 2nd edition, reprinted. Oliver and Boyd, London.
Kabaila, P. and Giri, K. (2009) Confidence intervals in regression utilizing prior information. Journal of Statistical Planning and Inference, 139, 3419 - 3429.