binom (version 1.0-4)

binom.optim: Optimal binomial confidence intervals

Description

Uses optimization to minimize the integrated mean squared error between the calculated coverage and the desired confidence level for a given binomial confidence interval.

Usage

binom.optim(n, conf.level = 0.95, method = binom.lrt,
            k = n%/%2 + 1, p0 = 0, transform = TRUE,
            plot = FALSE, tol = .Machine$double.eps^0.5,
            start = NULL, ...)

Arguments

n

The number of independent trials in the binomial experiment.

conf.level

The level of confidence to be used in the confidence interval.

method

The method used to estimate the confidence interval.

k

See Details.

p0

The minimum probability of success to allow in the optimization. See Details.

transform

logical; If TRUE the optimizer will do an unconstrained optimization on the signficance probability in the logit space.

plot

logical; If TRUE the results are sent to binom.plot.

tol

The minimum significance level to allow in the optimization. See Details.

start

A starting value on the optimal confidence level.

...

Additional arguments to pass to optim.

Value

• A list with the following elements:
  • par
  {Final confidence levels. The length of this vector is k.}

• value
  The final minimized value from optim.
• counts
  The number of function and gradient calls from optim.
• convergence
  Convergence code from optim.
• message
  Any message returned by the L-BFGS-B or BFGS optimizer.
• confint
  A data.frame returned from a call to method using the optimized confidence levels.

Details

This function minimizes the squared error between the expected coverage probability and the desired confidence level.

$$\alpha_{opt}=\arg\min_{\alpha}\int_{0}^{1}[C(p,n)-(1-\alpha)^2dp$$

The optimizer will adjust confidence intervals for all x = 0 to n depending on the value of k provided. If k is one, only the confidence levels for x = 0 and n are adjusted. If k = [n/2] then all confidence intervals are adjusted. This assumes the confidence intervals are the same length for x = x[k] and x[n - k + 1], which is the case for all methods provided in this package except binom.cloglog.

See Also

binom.confint, binom.plot, binom.coverage, optim

Examples

binom.optim(10, k = 1) ## determine optimal significance for x = 0, 10 only
binom.optim(3, method = binom.wilson) ## determine optimal significance for all x