mdd {EDMeasure} R Documentation

## Martingale Difference Divergence

### Description

`mdd` measures conditional mean dependence of `Y` given `X`, where each contains one variable (univariate) or more variables (multivariate).

### Usage

```mdd(X, Y, compute = "C", center = "U")
```

### Arguments

 `X` A vector, matrix or data frame, where rows represent samples, and columns represent variables. `Y` A vector, matrix or data frame, where rows represent samples, and columns represent variables. `compute` The method for computation, including `C`: computation implemented in C code; `R`: computation implemented in R code. `center` The approach for centering, including `U`: U-centering which leads to an unbiased estimator; `D`: double-centering which leads to a biased estimator.

### Value

`mdd` returns the squared martingale difference divergence of `Y` given `X`.

### References

Shao, X., and Zhang, J. (2014). Martingale difference correlation and its use in high-dimensional variable screening. Journal of the American Statistical Association, 109(507), 1302-1318. http://dx.doi.org/10.1080/01621459.2014.887012.

Park, T., Shao, X., and Yao, S. (2015). Partial martingale difference correlation. Electronic Journal of Statistics, 9(1), 1492-1517. http://dx.doi.org/10.1214/15-EJS1047.

### Examples

```# X, Y are vectors with 10 samples and 1 variable
X <- rnorm(10)
Y <- rnorm(10)

mdd(X, Y, compute = "C")
mdd(X, Y, compute = "R")

# X, Y are 10 x 2 matrices with 10 samples and 2 variables
X <- matrix(rnorm(10 * 2), 10, 2)
Y <- matrix(rnorm(10 * 2), 10, 2)

mdd(X, Y, center = "U")
mdd(X, Y, center = "D")
```

[Package EDMeasure version 1.2.0 Index]