HufferPark {ellipticalsymmetry} | R Documentation |

Pearson chi-square type test for elliptical symmetry.

```
HufferPark(X, c, R = NA, sector = "orthants", g = NA, nJobs = -1)
```

`X` |
A numeric matrix. |

`c` |
The number of spherical shells that are used to divide the space. |

`R` |
The number of bootstrap replicates. |

`sector` |
A string that specifies the type of sectors used to divide the space. Currently supported options are |

`g` |
A parameter that is used if |

`nJobs` |
The number of CPU cores used for the calculation. The default value -1 indicates that all cores except one are used. |

Huffer and Park (2007) propose a Pearson chi-square type test with multi-dimensional cells.
After dividing the space into `c`

spherical shells and `g`

sectors (in total `gc`

cells),
and after determining the observed cell counts, the test statistic is easily computed.
`sector`

is an option that allows the user to specify the type of sectors used to divide the space.
Currently supported options are `"orthants"`

, `"permutations"`

and `"bivariateangles"`

,
the last one being available only in dimension 2. The `g`

argument indicates the number of sectors.
The user has to choose `g`

only if `sector = "bivariateangles"`

and it denotes the number of regions used to divide the plane.
In this case, regions consist of points whose angle in polar coordinates is between `2(m-1)\pi/g`

and `2m\pi/g`

for `m`

in `(1,..., g)`

.
If `sector`

is set to `"orthants"`

, then `g`

is fixed and equal to `2^d`

, while for `sector = "permutations"`

`g`

is `d`

!.
No matter what type of sectors is chosen, the user has to specify the number of spherical shells that are used to divide the space, which is `c`

.
The value of `c`

should be such that the average cell counts `n/(gc)`

are not too small.

The asymptotic distribution is available only under `sector = "orthants"`

when the underlying distribution is close to normal.
Otherwise, bootstrap procedures are required and the user can freely choose the number of bootstrap replicates, denoted as `R`

.
Note that by default `sector`

is set to `"orthants"`

and `R = NA`

, which means that the non-bootstrap version of the test
will be performed unless the user specifies `R`

.

An object of class `"htest"`

containing the following components:

`statistic` |
The value of the test statistic. |

`pvalue` |
The p-value of the test. |

`alternative` |
A character string describing the alternative hypothesis. |

`method` |
A character string indicating what type of test was performed. |

Huffer, Fred W., & Park, C., (2007). A test for elliptical symmetry. *Journal of Multivariate Analysis*, **98**(2), 256-281.

```
## sepal width and length of the versicolor subset of the Iris data
X = datasets::iris[51:100,1:2]
## the non-bootstrap test
HufferPark(X, c = 2)
## the bootstrap tests
HufferPark(X, c = 2, R = 10, sector="orthants", nJobs=2)
HufferPark(X, c = 2, R = 10, sector="bivariateangles", g = 3, nJobs=2)
HufferPark(X, c = 2, R = 10, sector="permutations", nJobs=2)
```

[Package *ellipticalsymmetry* version 0.1.2 Index]