Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

1 2 | ```
dcorT.test(x, y)
dcorT(x, y)
``` |

`x` |
data or distances of first sample |

`y` |
data or distances of second sample |

`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 ≥q 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.

`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 |

`dcor.t`

and `dcor.ttest`

are deprecated.

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

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.

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.

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.

doi: 10.1214/09-AOAS312

1 2 3 4 |

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