cistandard: Compute the standard confidence interval
In ciuupi: Confidence Intervals Utilizing Uncertain Prior Information

Description Usage Arguments Details Value References Examples

Compute the standard confidence interval

1	cistandard(a, x, y, alpha, sig = NULL)

`a`	A vector used to specify the parameter of interest
`x`	A known n by p matrix
`y`	A known n-vector of responses
`alpha`	1 - `alpha` is the nominal coverage probability of the confidence interval
`sig`	Standard deviation of the random error. If a value is not specified, `sig` will be estimated from the data.

Suppose that

Y = X β + ε

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 has a multivariate normal distribution with mean vector 0 and variance sig^2 times the n by n identity matrix. Then cistandard will compute the standard confidence interval for a' β.

In the example below we use the data set described in Table 7.5 of Box et al. (1963). A description of the parameter of interest is given in Dicsussion 5.8, p.3426 of Kabaila and Giri (2009).

The standard confidence interval

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.

y <- c(87.2, 88.4, 86.7, 89.2)
x1 <- c(-1, 1, -1, 1)
x2 <- c(-1, -1, 1, 1)
x <- cbind(rep(1, 4), x1, x2, x1*x2)
a <- c(0, 2, 0, -2)

# Calculate the standard 95% confidence interval when sigma = 0.8
res <- cistandard(a, x, y, 0.05, sig = 0.8)
res