# logconTwoSample: Compute p-values for two-sample test based on log-concave CDF... In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

## 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

 1 2 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.

## Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

## References

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

 1 2 3 4 5 6 7 8 ## 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) 

logcondens documentation built on May 2, 2019, 6:11 a.m.