R: Computations for Graphical GOF Test via Pairwise Rosenblatt...

ggraph-tools {copula} | R Documentation

## Computations for Graphical GOF Test via Pairwise Rosenblatt Transforms

### Description

Tools for computing a graphical goodness-of-fit (GOF) test based on pairwise Rosenblatt transformed data.

`pairwiseCcop()`

  computes a (n,d,d)-`array` which contains pairwise Rosenblatt-transformed data.

`pairwiseIndepTest()`

  takes such an array as input and computes a (d,d)-`matrix` of test results from pairwise tests of independence (as by `indepTest()`).

`pviTest()`

  can be used to extract the matrix of p-values from the return matrix of `pairwiseIndepTest()`.

`gpviTest()`

  takes such a matrix of p-values and computes a global p-value with the method provided.

### Usage

    pairwiseCcop(u, copula, ...)
    pairwiseIndepTest(cu.u, N=256,
            iTest = indepTestSim(n, p=2, m=2, N=N, verbose = idT.verbose, ...),
            verbose=TRUE, idT.verbose = verbose, ...)

     pviTest(piTest)
    gpviTest(pvalues, method=p.adjust.methods, globalFun=min)

### Arguments

`u` | (n,d)-`matrix` of copula data.
`copula` | copula object used for the Rosenblatt transform (H[0] copula).
`...` | additional arguments passed to the internal function which computes the conditional copulas (for `pairwiseCcop()`). Can be used to pass, for example, the degrees of freedom parameter `df` for t-copulas. For `pairwiseIndepTest()`, ... are passed to `indepTestSim()`.
`cu.u` | (n,d,d)-`array` as returned by `pairwiseCcop()`.
`N` | argument of `indepTestSim()`.
`iTest` | the result of (a version of) `indepTestSim()`; as it does not depend on the data, and is costly to compute, it can be computed separately and passed here.
`verbose` | `integer` (or `logical`) indicating if and how much progress should be printed during the computation of the tests for independence.
`idT.verbose` | logical, passed as `verbose` argument to `indepTestSim()`.
`piTest` | (d,d)-`matrix` of `indepTest` objects as returned by `pairwiseIndepTest()`.
`pvalues` | (d,d)-`matrix` of p-values.
`method` | `character` vector of adjustment methods for p-values; see `p.adjust.methods` for more details.
`globalFun` | `function` determining how to compute a global p-value from a matrix of pairwise adjusted p-values.

### Value

pairwiseCcop

  (n,d,d)-`array` `cu.u` with `cu.u[i,j]` containing C(u[,i]|u[,j]) for i!=j and u[,i] for i=j.

pairwiseIndepTest

  (d,d)-`matrix` of lists with test results as returned by `indepTest()`. The test results correspond to pairwise tests of independence as conducted by `indepTest()`.

pviTest

  (d,d)-`matrix` of p-values.

gpviTest

  global p-values for the specified methods.

### Note

If `u` are distributed according to or “perfectly” sampled from a copula, p-values on GOF tests for that copula should be uniformly distributed in [0,1].

### References

Hofert and Mächler (2014), see `pairsRosenblatt`.

### See Also

`pairsRosenblatt` for where these tools are used, including `demo(gof_graph)` for examples.

### Examples

    ## demo(gof_graph)

[Package copula version 1.0-1 Index]