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

View source: R/modeHuntingBlock.r

Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed via the block procedure.

1 2 | ```
modeHuntingBlock(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 `modeHuntingBlock`

uses the test statistic *T^+_n({\bf X}, \mathcal{B}_r)*,
where *\mathcal{B}_r* contains all intervals of Block *r*, *r=1,…,\#blocks*.
Critical values for each block individually are received via finding an *\tilde α* such that

*P(B_n({\bf{X}}) > q_{r,\tilde α / (r+tail)^γ} \ for \ at \ least \ one \ r) ≤ α,*

where *q_{r,α}* is the *(1-α)*–quantile of the distribution of *T^+_n({\bf X}, \mathcal{B}_r).*
We then define the sets *\mathcal{D}^\pm(α)* as

*\mathcal{D}^\pm(α) := \Bigl\{\mathcal{I}_{jk} \ : \ \pm T_{jk}({\bf{X}}) > q_{r,\tilde α / (r+tail)^γ} \, , \ r = 1,… \#blocks\Bigr\}.*

Note that *γ* and *tail* are automatically determined by *crit.vals*.

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 |

Critical values for some combinations of *n* and *α* are provided in the
data sets `cvModeBlock`

. 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`

, `modeHuntingApprox`

, and `cvModeBlock`

.

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

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