ci_standard {ciuupi} | R Documentation |
For given observed response vector
, compute
the standard
confidence interval
Description
If is provided then compute the standard
confidence interval for
. If
is not provided
then, as long as
, replace
by its estimate
to compute an approximate
confidence interval for
.
Usage
ci_standard(a, X, y, alpha, sig = NULL)
Arguments
a |
The vector used to specify the parameter of interest
|
X |
The known |
y |
The |
alpha |
|
sig |
Standard deviation of the random error.
If a value is not specified then, provided that |
Details
Suppose that
where is a random
-vector of responses,
is a known
matrix with linearly independent columns,
is an unknown parameter
-vector, and
, with
assumed known.
Suppose that the parameter of interest is
.
The R function
ci_standard
computes the standard
confidence interval for
.
The example below is described in Discussion 5.8 on
p.3426 of Kabaila and Giri (2009). This example is obtained
by extracting a factorial data set from the
factorial data set described in Table 7.5
of Box et al. (1963).
Value
If is provided then a data frame of the lower and upper
endpoints of the standard
confidence interval
for
. If
is not provided then, as long as
, a data frame of the
lower and upper endpoints of
an approximation to this confidence interval.
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.
Examples
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)
ci_standard(a, X, y, 0.05, sig = 0.8)