R: Compute p-values for two-sample test based on log-concave CDF...
logconTwoSample
R Documentation
Compute p-values for two-sample test based on log-concave CDF estimates
Description
Compute p-values for a test for the null hypothesis of equal CDFs of two samples. The test
statistic is reminiscient of Kolmogorv-Smirnov's, but instead of computing it for the empirical CDFs, this function
computes it based on log-concave estimates for the CDFs.
Usage
logconTwoSample(x, y, which = c("MLE", "smooth"), M = 999,
n.grid = 500, display = TRUE, seed0 = 1977)
Arguments
x
First data sample.
y
Second data sample.
which
Indicate for which type of estimate the test statistic should be computed.
M
Number of permutations.
n.grid
Number of grid points in computation of maximal difference between smoothed log-concave CDFs. See maxDiffCDF for details.
display
If TRUE progress of computations is shown.
seed0
Set seed to reproduce results.
Details
Given two i.i.d. samples x_1, …, x_{n_1} and y_1, …, y_{n_2} this function computes a permutation
test p-value that provides evidence against the null hypothesis
H_0 : F_1 = F_2
where F_1, F_2 are the CDFs of the samples, respectively. A test either based on the log-concave MLE or on its
smoothed version (see Duembgen and Rufibach, 2009, Section 3) are provided. Note that computation of the smoothed
version takes considerably more time.
Value
p.value
A two dimensional vector containing the p-values.
test.stat.orig
The test statistics for the original samples.
test.stats
A M \times 2 matrix containing the test statistics for all the permutations.
Warning
Note that the algorithm that finds the maximal difference for the smoothed estimate is of approximative
nature only. It may fail for very large sample sizes.
Duembgen, L. and Rufibach, K. (2009)
Maximum likelihood estimation of a log–concave density and its distribution function: basic properties and uniform consistency.
Bernoulli, 15(1), 40–68.
Duembgen, L. and Rufibach, K. (2011)
logcondens: Computations Related to Univariate Log-Concave Density Estimation.
Journal of Statistical Software, 39(6), 1–28. http://www.jstatsoft.org/v39/i06
Examples
## Not run:
n1 <- 30
n2 <- 25
x <- rgamma(n1, 2, 1)
y <- rgamma(n2, 2, 1) + 1
twosample <- logconTwoSample(x, y, which = c("MLE", "smooth")[1], M = 999)
## End(Not run)