Distance correlation t-test of multivariate independence for high dimension.

```
dcorT.test(x, y)
dcorT(x, y)
```

`dcorT`

returns the dcor t statistic, and
`dcorT.test`

returns a list with class `htest`

containing

- method
description of test

- statistic
observed value of the test statistic

- parameter
degrees of freedom

- estimate
(bias corrected) squared dCor(x,y)

- p.value
p-value of the t-test

- data.name
description of data

- x
data or distances of first sample

- y
data or distances of second sample

Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely

`dcorT.test`

performs a nonparametric t-test of
multivariate independence in high dimension (dimension is close to
or larger than sample size). As dimension goes to infinity, the
asymptotic distribution of the test statistic is approximately Student t with \(n(n-3)/2-1\) degrees of freedom and for \(n \geq 10\) the statistic is approximately distributed as standard normal.

The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values.

The t statistic (dcorT) is a transformation of a bias corrected version of distance correlation (see SR 2013 for details).

Large values (upper tail) of the dcorT statistic are significant.

Szekely, G.J. and Rizzo, M.L. (2013). The distance correlation t-test of independence in high dimension. *Journal of Multivariate Analysis*, Volume 117, pp. 193-213.

tools:::Rd_expr_doi("10.1016/j.jmva.2013.02.012")

Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007),
Measuring and Testing Dependence by Correlation of Distances,
*Annals of Statistics*, Vol. 35 No. 6, pp. 2769-2794.

tools:::Rd_expr_doi("10.1214/009053607000000505")

Szekely, G.J. and Rizzo, M.L. (2009),
Brownian Distance Covariance,
*Annals of Applied Statistics*,
Vol. 3, No. 4, 1236-1265.

tools:::Rd_expr_doi("10.1214/09-AOAS312")

`bcdcor`

`dcov.test`

`dcor`

`DCOR`

```
x <- matrix(rnorm(100), 10, 10)
y <- matrix(runif(100), 10, 10)
dcorT(x, y)
dcorT.test(x, y)
```

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