README.md

In jeffjyan/MDD: Conditional Mean Independence Testing via Martingale Difference Divergence

MDD: Conditional Mean Independence Testing via Martingale Difference Divergence

The R package MDD implements conditional mean independence testing based on martingale difference divergence, using permutation and wild Bootstrap.

Introduction and Motivation

Martingale difference divergence (MDD) and martingale dfference correlation (MDC) are intended to measure departure from the relationship E(Y|X) = E(Y) a.s.. For example, in linear models, an important problem is to assess whether X contributes to the conditional mean of Y, i.e., H0 : E(Y|X) = E(Y). Since if H0 is supported by the data, then there is no need to pursue a regression model for the mean of Y given X.

Installation

require(devtools)
devtools::install_github("jeffjyan/MDD")
library(MDD)

Example

# Data illustration
X <- mtcars$wt
Y <- mtcars$mpg
mdd_test_perm(X, Y)$p_value
mdd_test_boot(X, Y)$p_value

X <- mtcars$am
Y <- mtcars$carb
mdd_test_perm(X, Y)$p_value
mdd_test_boot(X, Y)$p_value

X <- iris[1:50, c(1,3)]
Y <- iris[1:50, c(2,4)]
mdd_test_perm(X, Y)$p_value
mdd_test_boot(X, Y)$p_value


# Simulation
X <- rnorm(30)
Y <- rpois(30, lambda = 1)
mdd_test_perm(X, Y)$p_value
mdd_test_boot(X, Y)$p_value

X <- rnorm(30)
Y <- X^2
mdd_test_perm(X, Y)$p_value
mdd_test_boot(X, Y)$p_value

Reference

Székely, Gábor J., Maria L. Rizzo, and Nail K. Bakirov. "Measuring and testing dependence by correlation of distances." The annals of statistics 35.6 (2007): 2769-2794.

Shao, Xiaofeng, and Jingsi Zhang. "Martingale difference correlation and its use in high-dimensional variable screening." Journal of the American Statistical Association 109.507 (2014): 1302-1318.

Park, Trevor, Xiaofeng Shao, and Shun Yao. "Partial martingale difference correlation." Electronic Journal of Statistics 9.1 (2015): 1492-1517.

Chung Eun Lee, Xianyang Zhang, and Xiaofeng Shao. Testing the conditional mean independence for functional data. Biometrika, forthcoming, 2019.

jeffjyan/MDD documentation built on Dec. 9, 2019, 12:16 a.m.