modeHunting {modehunt} | R Documentation |
Multiscale analysis of a density on all possible intervals
Description
Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed on all intervals spanned by two observations.
Usage
modeHunting(X.raw, lower = -Inf, upper = Inf, crit.vals, min.int = FALSE)
Arguments
X.raw |
Vector of observations. |
lower |
Lower support point of |
upper |
Upper support point of |
crit.vals |
2-dimensional vector giving the critical values for the desired level. |
min.int |
If |
Details
In general, the methods modeHunting
, modeHuntingApprox
, and
modeHuntingBlock
compute for a given level and the corresponding
critical value
two sets of intervals
where for
and
are
appropriate critical values.
Specifically, the function modeHunting
computes based on the two
test statistics
and
using the set of all intervals spanned by two observations
:
We introduced the local test statistics
for local order statistics
the standard deviation and the additive correction term
for
.
If min.int = TRUE
, the set is replaced by the set
of its minimal elements. An interval
is called minimal if
contains no proper subset of
. 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
as precisely as possible, the intervals in
do not contain relevant information.
Value
Dp |
The set |
Dm |
The set |
Dp.noadd |
The set |
Dm.noadd |
The set |
Note
Critical values for modeHunting
and some combinations of and
are provided in the
data set
cvModeAll
. Critical values for other values of and
can be generated
using
criticalValuesAll
.
Parts of this function were derived from MatLab code provided on Lutz Duembgen's webpage,
http://www.staff.unibe.ch/duembgen.
Author(s)
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Guenther Walther, gwalther@stanford.edu,
www-stat.stanford.edu/~gwalther
References
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.
See Also
modeHuntingApprox
, modeHuntingBlock
, and cvModeAll
.
Examples
## for examples type
help("mode hunting")
## and check the examples there