modeHuntingApprox {modehunt} | R Documentation |
Multiscale analysis of a density on the approximating set of intervals
Description
Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed on the approximating set of intervals.
Usage
modeHuntingApprox(X.raw, lower = -Inf, upper = Inf,
d0 = 2, m0 = 10, fm = 2, crit.vals, min.int = FALSE)
Arguments
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 |
Details
See blocks
for details how is generated and
modeHunting
for
a proper introduction to the notation used here.
The function modeHuntingApprox
computes based on the two
test statistics
and
.
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 modeHuntingApprox
and some combinations of and
are
provided in the data set
cvModeApprox
. Critical values for other
values of and
can be generated using
criticalValuesApprox
.
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
modeHunting
, modeHuntingBlock
, and cvModeApprox
.
Examples
## for examples type
help("mode hunting")
## and check the examples there