Description Usage Arguments Details Value See Also Examples

Perform permutation test using various dependence measures, in which Xs are quantitative, Y are categorical, alpha is an exponent on Euclidean distance, sigma is kernel parameter in kernel methods and return the test statistic, critical value, p-value and decision of the test.

1 | ```
PermutationTest(x, y, method, sigma, alpha, M = 200, level = 0.05)
``` |

`x` |
data |

`y` |
label of data or univariate response variable |

`method` |
name of permutation test method and is chosen from one of the method list: dCov, dCor, KdCov, KdCor, gCov, gCor, KgCov, Kgcor |

`sigma` |
kernel parameter for kenerl methods |

`alpha` |
exponent on Euclidean distance, in (0,2), the default value = 1 |

`M` |
number of permutations |

`level` |
significance level of the test, the default value = 0.05 |

*H_0:* X and Y are independent *\Longleftrightarrow H_0: F(x|y=1)=F(x|Y=2)=...=F(x|Y=K)*

`PermutationTest`

compute the p-value value of a permutation test of a (Gini) distance covariance or correlation statistics.
It is a self-contained R function the measure of dependence statistics.

The p-value is obtained by a permutation procedure.
Let *\hat{ρ}(ν)* be the sample dependnce measure based on the orginal sample indexed by *ν=\{1,2,...,n\}*. Let *π(ν)* denote a permutation of the elements of *ν* and the corresponding *\hat{ρ}(π)* is computed for the permutated data on y labels.
Under the *{\cal H}_0*, *\hat{ρ}(ν)*
and *\hat{ρ}(π)* are identically distributed for every permutation *π* of *ν*.
Hence, based on *M* permutations, the critical value *q_{γ}* is estimated by the *(1-γ)100\%* sample
quantile of *\hat{ρ}(π_m)*, *m=1,...,M* and the p-value is estimated by the proportion of
*\hat{ρ}(π_m)* greater than *\hat{ρ}(ν)*. Usually *100≤q M≤q 1000* is sufficient for a good estimation on the critical value or p-value. The default value is *M=200*.

`PermutationTest`

returns the p-value, critical value and decision of the permutation test of a specified method.

`gCor`

`gCov`

`dCor`

`dCov`

`KgCov`

`KgCov`

`KdCov`

1 2 3 4 | ```
n = 50
x <- runif(n)
y <- c(rep(1,n/2),rep(2,n/2))
PermutationTest(x, y, method = "gCor", alpha = 2, M = 50 )
``` |

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