exchEVTest | R Documentation |

Test for assessing the exchangeability of the underlying bivariate copula when it is either extreme-value or left-tail decreasing. The test uses the nonparametric estimators of the Pickands dependence function studied by Genest and Segers (2009).

The test statistic is defined in the second reference.
An approximate p-value for the test statistic is obtained
by means of a *multiplier* technique if there are no ties in the
component series of the bivariate data, or by means of an appropriate
bootstrap otherwise.

exchEVTest(x, N = 1000, estimator = c("CFG", "Pickands"), ties = NA, ties.method = eval(formals(rank)$ties.method), m = 100, derivatives = c("Cn", "An"))

`x` |
a data matrix that will be transformed to pseudo-observations. |

`N` |
number of multiplier or boostrap iterations to be used to simulate realizations of the test statistic under the null hypothesis. |

`estimator` |
string specifying which nonparametric estimator of
the Pickands dependence function |

`ties` |
logical; if |

`ties.method` |
string specifying how ranks should be computed if
there are ties in any of the coordinate samples of |

`derivatives` |
a string specifying how the derivatives of the
unknown copula are estimated; can be either |

`m` |
integer specifying the size of the integration grid for the statistic. |

More details are available in the references.

An object of `class`

`htest`

which is a list,
some of the components of which are

`statistic` |
value of the test statistic. |

`pvalue` |
corresponding approximate p-value. |

Genest, C. and Segers, J. (2009)
Rank-based inference for bivariate extreme-value copulas.
*Annals of Statistics* **37**, 2990–3022.

Kojadinovic, I. and Yan, J. (2012)
A nonparametric test of exchangeability for extreme-value and left-tail
decreasing bivariate copulas.
*The Scandinavian Journal of Statistics* **39:3**, 480–496.

Kojadinovic, I. (2017). Some copula inference procedures adapted to
the presence of ties. *Computational Statistics and Data
Analysis* **112**, 24–41, https://arxiv.org/abs/1609.05519.

`exchTest`

, `radSymTest`

, `gofCopula`

.

## Data from an exchangeable left-tail decreasing copulas exchEVTest(rCopula(200, gumbelCopula(3))) exchEVTest(rCopula(200, claytonCopula(3))) ## An asymmetric Khoudraji-Gumbel-Hougaard copula kc <- khoudrajiCopula(copula1 = indepCopula(), copula2 = gumbelCopula(4), shapes = c(0.4, 0.95)) exchEVTest(rCopula(200, kc))

copula documentation built on Feb. 16, 2023, 8:46 p.m.

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