modeHuntingBlock {modehunt} | R Documentation |
Simultanous confidence statements for the existence and location of local increases and decreases of a density f, computed via the block procedure.
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 f, if known. |
upper |
Upper support point of f, if known. |
d0 |
Initial parameter for the grid resolution. |
m0 |
Initial parameter for the number of observations in one block. |
fm |
Factor by which m is increased from block to block. |
crit.vals |
2-dimensional vector giving the critical values for the desired level. |
min.int |
If min.int = TRUE , the set of minimal intervals is output, otherwise all intervals with a test
statistic above the critical value (in their respective block) are given. |
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)^gamma} 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)^gamma} , , r = 1,... #blocksBigr}.
Note that gamma 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 mathcal{D}^+(α) (or bf{D}^+(α)). |
Dm |
The set mathcal{D}^-(α) (or bf{D}^-(α)). |
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
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. (2007). A general criterion for multiscale inference. Preprint, Department of Statistics, Stanford University.
modeHunting
, modeHuntingApprox
, and cvModeBlock
.
## for examples type help("mode hunting") ## and check the examples there