pdcor: Partial distance correlation and covariance In energy: E-Statistics: Multivariate Inference via the Energy of Data

Description

Partial distance correlation pdcor, pdcov, and tests.

Usage

 ```1 2 3 4``` ``` pdcov.test(x, y, z, R) pdcor.test(x, y, z, R) pdcor(x, y, z) pdcov(x, y, z) ```

Arguments

 `x` data matrix or dist object of first sample `y` data matrix or dist object of second sample `z` data matrix or dist object of third sample `R` replicates for permutation test

Details

`pdcor(x, y, z)` and `pdcov(x, y, z)` compute the partial distance correlation and partial distance covariance, respectively, of x and y removing z.

A test for zero partial distance correlation (or zero partial distance covariance) is implemented in `pdcor.test`, and `pdcov.test`.

If the argument is a matrix, it is treated as a data matrix and distances are computed (observations in rows). If the arguments are distances or dissimilarities, they must be distance (`dist`) objects. For symmetric, zero-diagonal dissimilarity matrices, use `as.dist` to convert to a `dist` object.

Value

Each test returns an object of class `htest`.

Author(s)

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

References

Szekely, G.J. and Rizzo, M.L. (2014), Partial Distance Correlation with Methods for Dissimilarities. Annals of Statistics, Vol. 42 No. 6, 2382-2412.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27``` ``` n = 30 R <- 199 ## mutually independent standard normal vectors x <- rnorm(n) y <- rnorm(n) z <- rnorm(n) pdcor(x, y, z) pdcov(x, y, z) pdcov.test(x, y, z, R=R) print(pdcor.test(x, y, z, R=R)) if (require(MASS)) { p = 4 mu <- rep(0, p) Sigma <- diag(p) ## linear dependence y <- mvrnorm(n, mu, Sigma) + x print(pdcov.test(x, y, z, R=R)) ## non-linear dependence y <- mvrnorm(n, mu, Sigma) * x print(pdcov.test(x, y, z, R=R)) } ```

Example output

```     pdcor
0.03380488
[1] 0.0109811

pdcov test

data:  replicates 199
n V^* = 0.32943, p-value = 0.235
sample estimates:
pdcor
0.03380488

pdcor test

data:
pdcor = 0.033805, p-value = 0.205
sample estimates:
pdcor
0.03380488

pdcov test

data:  replicates 199
n V^* = 12.376, p-value = 0.005
sample estimates:
pdcor
0.6372653

pdcov test

data:  replicates 199
n V^* = 1.7541, p-value = 0.005
sample estimates:
pdcor
0.2285614
```

energy documentation built on Feb. 22, 2021, 5:08 p.m.