Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/modeHuntingApprox.r

Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed on the approximating set of intervals.

1 2 | ```
modeHuntingApprox(X.raw, lower = -Inf, upper = Inf,
d0 = 2, m0 = 10, fm = 2, crit.vals, min.int = FALSE)
``` |

`X.raw` |
Vector of observations. |

`lower` |
Lower support point of |

`upper` |
Upper support point of |

`d0` |
Initial parameter for the grid resolution. |

`m0` |
Initial parameter for the number of observations in one block. |

`fm` |
Factor by which |

`crit.vals` |
2-dimensional vector giving the critical values for the desired level. |

`min.int` |
If |

See `blocks`

for details how *\mathcal{I}_{app}* is generated and `modeHunting`

for
a proper introduction to the notation used here.
The function `modeHuntingApprox`

computes *\mathcal{D}^\pm(α)* based on the two
test statistics *T_n^+({\bf{X}}, \mathcal{I}_{app})* and *T_n({\bf{X}}, \mathcal{I}_{app})*.

If `min.int = TRUE`

, the set *\mathcal{D}^\pm(α)* is replaced by the set *{\bf{D}}^\pm(α)*
of its *minimal elements*. An interval *J \in \mathcal{D}^\pm(α)* is called *minimal* if
*\mathcal{D}^\pm(α)* contains no proper subset of *J*. This *minimization* post-processing
step typically massively reduces the number of intervals. If we are mainly interested in locating the ranges
of increases and decreases of *f* as precisely as possible, the intervals in
*\mathcal{D}^\pm(α) \setminus \bf{D}^\pm(α)* do not contain relevant information.

`Dp` |
The set |

`Dm` |
The set |

`Dp.noadd` |
The set |

`Dm.noadd` |
The set |

Critical values for `modeHuntingApprox`

and some combinations of *n* and *α* are
provided in the data set `cvModeApprox`

. Critical values for other
values of *n* and *α* can be generated using `criticalValuesApprox`

.

Kaspar Rufibach, kaspar.rufibach@gmail.com,

http://www.kasparrufibach.ch

Guenther Walther, gwalther@stanford.edu,

www-stat.stanford.edu/~gwalther

Duembgen, L. and Walther, G. (2008).
Multiscale Inference about a density.
*Ann. Statist.*, **36**, 1758–1785.

Rufibach, K. and Walther, G. (2010).
A general criterion for multiscale inference.
*J. Comput. Graph. Statist.*, **19**, 175–190.

`modeHunting`

, `modeHuntingBlock`

, and `cvModeApprox`

.

1 2 3 | ```
## for examples type
help("mode hunting")
## and check the examples there
``` |

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