MKinfer (version 0.6)

quantileCI: Confidence Intervals for Quantiles

Description

These functions can be used to compute confidence intervals for quantiles (including median).

Usage

quantileCI(x, prob = 0.5, conf.level = 0.95, method = "exact",
           R = 9999, bootci.type = c("norm", "basic", "perc", "bca"), 
           minLength = FALSE, na.rm = FALSE, 
           alternative = c("two.sided", "less", "greater"))
medianCI(x, conf.level = 0.95, method = "exact",
         R = 9999, bootci.type = c("norm", "basic", "perc", "bca"), 
         minLength = FALSE, na.rm = FALSE, 
         alternative = c("two.sided", "less", "greater"))
madCI(x, conf.level = 0.95, method = "exact", minLength = FALSE,
      R = 9999, bootci.type = c("norm", "basic", "perc", "bca"), 
      na.rm = FALSE, constant = 1.4826, 
      alternative = c("two.sided", "less", "greater"))

Value

A list with components

estimate

the sample quantile.

CI

a confidence interval for the sample quantile.

Arguments

x

numeric data vector

prob

quantile

conf.level

confidence level

method

character string specifing which method to use; see details.

minLength

logical, see details

R

number of bootstrap replicates.

bootci.type

type of bootstrap interval; see boot.ci.

na.rm

logical, remove NA values.

constant

scale factor (see mad).

alternative

a character string specifying one- or two-sided confidence intervals. Must be one of "two.sided" (default), "greater" or "less" (one-sided intervals). You can specify just the initial letter.

Author

Matthias Kohl

Details

The exact confidence interval (method = "exact") is computed using binomial probabilities; see Section 6.8.1 in Sachs and Hedderich (2009). If the result is not unique, i.e. there is more than one interval with coverage proability closest to conf.level, then a matrix of confidence intervals is returned. If minLength = TRUE, an exact confidence interval with minimum length is returned.

The asymptotic confidence interval (method = "asymptotic") is based on the normal approximation of the binomial distribution; see Section 6.8.1 in Sachs and Hedderich (2009).

In case of discrete data, there are alternative bootstrap approaches that might give better results; see Jentsch and Leucht (2016).

References

L. Sachs and J. Hedderich (2009). Angewandte Statistik. Springer.

C. Jentsch and A. Leucht (2016). Bootstrapping sample quantiles of discrete data. Ann Inst Stat Math, 68: 491-539.

See Also

binom.test, binconf

Examples

## To get a non-trivial exact confidence interval for the median
## one needs at least 6 observations
set.seed(123)
x <- rnorm(8)
## exact confidence interval not unique
medianCI(x)
madCI(x)

## minimum length exact confidence interval
medianCI(x, minLength = TRUE)
madCI(x, minLength = TRUE)

## asymptotic confidence interval
medianCI(x, method = "asymptotic")
madCI(x, method = "asymptotic")

## bootstrap confidence interval
x <- rnorm(50)
medianCI(x)
medianCI(x, method = "asymptotic")
## (R = 999 to reduce computation time for R checks)
medianCI(x, method = "boot", R = 999)

madCI(x)
madCI(x, method = "asymptotic")
## (R = 999 to reduce computation time for R checks)
madCI(x, method = "boot", R = 999)

## confidence interval for quantiles
quantileCI(x, prob = 0.25)
quantileCI(x, prob = 0.25, method = "asymptotic")

quantileCI(x, prob = 0.75)
## (R = 999 to reduce computation time for R checks)
quantileCI(x, prob = 0.75, method = "boot", R = 999)

## one-sided
quantileCI(x, prob = 0.75, alternative = "greater")
medianCI(x, alternative = "less", method = "asymptotic")
madCI(x, alternative = "greater", method = "boot", R = 999)