modeHuntingBlock {modehunt} | R Documentation |
Multiscale analysis of a density via block procedure
Description
Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed via the block procedure.
Usage
modeHuntingBlock(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 modeHuntingBlock
uses the test statistic ,
where
contains all intervals of Block
,
.
Critical values for each block individually are received via finding an
such that
where is the
–quantile of the distribution of
We then define the sets
as
Note that and
are automatically determined by
.
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 |
Note
Critical values for some combinations of and
are provided in the
data sets
cvModeBlock
. 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
, modeHuntingApprox
, and cvModeBlock
.
Examples
## for examples type
help("mode hunting")
## and check the examples there