norm.ci {boot}  R Documentation 
Normal Approximation Confidence Intervals
Description
Using the normal approximation to a statistic, calculate equitailed twosided confidence intervals.
Usage
norm.ci(boot.out = NULL, conf = 0.95, index = 1, var.t0 = NULL,
t0 = NULL, t = NULL, L = NULL, h = function(t) t,
hdot = function(t) 1, hinv = function(t) t)
Arguments
boot.out 
A bootstrap output object returned from a call to 
conf 
A scalar or vector containing the confidence level(s) of the required interval(s). 
index 
The index of the statistic of interest within the output of a call to

var.t0 
The variance of the statistic of interest. If it is not supplied then

t0 
The observed value of the statistic of interest. If it is missing then it is
taken from 
t 
Bootstrap replicates of the variable of interest. These are used to estimate
the variance of the statistic of interest if 
L 
The empirical influence values for the statistic of interest. These are
used to calculate 
h 
A function defining a monotonic transformation, the intervals are
calculated on the scale of 
hdot 
A function of one argument returning the derivative of 
hinv 
A function, like 
Details
It is assumed that the statistic of interest has an approximately
normal distribution with variance var.t0
and so a confidence
interval of length 2*qnorm((1+conf)/2)*sqrt(var.t0)
is found.
If boot.out
or t
are supplied then the interval is
biascorrected using the bootstrap bias estimate, and so the interval
would be centred at 2*t0mean(t)
. Otherwise the interval is
centred at t0
.
Value
If length(conf)
is 1 then a vector containing the confidence
level and the endpoints of the interval is returned. Otherwise, the
returned value is a matrix where each row corresponds to a different
confidence level.
Note
This function is primarily designed to be called by boot.ci
to
calculate the normal approximation after a bootstrap but it can also be
used without doing any bootstrap calculations as long as t0
and
var.t0
can be supplied. See the examples below.
References
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
See Also
Examples
# In Example 5.1 of Davison and Hinkley (1997), normal approximation
# confidence intervals are found for the airconditioning data.
air.mean < mean(aircondit$hours)
air.n < nrow(aircondit)
air.v < air.mean^2/air.n
norm.ci(t0 = air.mean, var.t0 = air.v)
exp(norm.ci(t0 = log(air.mean), var.t0 = 1/air.n)[2:3])
# Now a more complicated example  the ratio estimate for the city data.
ratio < function(d, w)
sum(d$x * w)/sum(d$u *w)
city.v < var.linear(empinf(data = city, statistic = ratio))
norm.ci(t0 = ratio(city,rep(0.1,10)), var.t0 = city.v)