# CvM.stat: Cramer - von Mises statistics In ignaciomsarmiento/RATest: Randomization Tests

## Description

Calculates the Cramer-von Mises test statistic

T(S_n)=\frac{1}{2q}∑_{i=1}^{2q}≤ft(H^-_n(S_{n,i})-H^+_n(S_{n,i})\right)^2

where H^-_n(\cdot) and H^+_n(\cdot) are the empirical CDFs of the the sample of baseline covariates close to the cutoff from the left and right, respectively. See equation (12) in Canay and Kamat (2017).

## Usage

 1 CvM.stat(Sn) 

## Arguments

 Sn Numeric. The pooled sample of induced order statistics. The first column of S can be viewed as an independent sample of W conditional on Z being close to zero from the left. Similarly, the second column of S can be viewed as an independent sample of W conditional on Z being close to the cutoff from the right. See section 3 in Canay and Kamat (2017).

## Value

Returns the numeric value of the Cramer - von Mises test statistic.

## Author(s)

Maurcio Olivares Gonzalez

Ignacio Sarmiento Barbieri

## References

Canay, I and Kamat V, (2017) Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design. http://faculty.wcas.northwestern.edu/~iac879/wp/RDDPermutations.pdf

ignaciomsarmiento/RATest documentation built on Dec. 9, 2018, 8:05 a.m.