# dcor.xy: Distance Correlation Statistic and t-Test In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 dcor.xy R Documentation

## Distance Correlation Statistic and t-Test

### Description

Distance correlation t-test of multivariate and functional independence (wrapper functions of energy package).

### Usage

```dcor.xy(x, y, test = TRUE, metric.x, metric.y, par.metric.x, par.metric.y, n)

dcor.dist(D1, D2)

bcdcor.dist(D1, D2, n)

dcor.test(D1, D2, n)
```

### Arguments

 `x` data (fdata, matrix or data.frame class) of first sample. `y` data (fdata, matrix or data.frame class) of second sample. `test` if TRUE, compute bias corrected distance correlation statistic and the corresponding t-test, else compute distance correlation statistic. `metric.x, metric.y` Name of metric or semi-metric function used for compute the distances of `x` and `y` object respectively. By default, `metric.lp` for functional data and `metric.dist` for multivariate data. `par.metric.x, par.metric.y` List of parameters for the corresponding metric function. `n` The sample size used in bias corrected version of distance correlation, by default is the number of rows of `x`. `D1` Distances of first sample (x data). `D2` Distances of second sample (y data).

### Details

These wrapper functions extend the functions of the `energy` package for multivariate data to functional data. Distance correlation is a measure of dependence between random vectors introduced by Szekely, Rizzo, and Bakirov (2007). `dcor.xy` performs a nonparametric t-test of multivariate or functional independence in high dimension. The 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. Wrapper function of `energy:::dcor.ttest`. The t statistic is a transformation of a bias corrected version of distance correlation (see SR 2013 for details). Large values (upper tail) of the t statistic are significant.
`dcor.test` similar to `dcor.xy` but only for distance matrix. `dcor.dist` compute distance correlation statistic. Wrapper function of `energy::dcor` but only for distance matrix `bcdcor.dist` compute bias corrected distance correlation statistic. Wrapper function of `energy:::bcdcor` but only for distance matrix.

### Value

`dcor.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 distance correlation `bcdcor(x,y)`

• `p.value` p-value of the t-test

• `data.name` description of data

`dcor.xy` returns the previous list with class `htest` and

• `D1` the distance matrix of `x`

• `D2` the distance matrix of `y`

`dcor.dist` returns the distance correlation statistic.

`bcdcor.dist` returns the bias corrected distance correlation statistic.

### Author(s)

Manuel Oviedo de la Fuente manuel.oviedo@udc.es and Manuel Febrero Bande

### References

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.

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.

`metric.lp` amd `metric.dist`.

### Examples

```## Not run:
x<-rproc2fdata(100,1:50)
y<-rproc2fdata(100,1:50)
dcor.xy(x, y,test=TRUE)
dx <- metric.lp(x)
dy <- metric.lp(y)
dcor.test(dx, dy)
bcdcor.dist(dx, dy)
dcor.xy(x, y,test=FALSE)
dcor.dist(dx, dy)

## End(Not run)

```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.