Given independent and identically distributed observations X(1), ..., X(n) from a density f, provides five methods to perform a multiscale analysis about f as well as the necessary critical values. The first method, introduced in Duembgen and Walther (2008), provides simultaneous confidence statements for the existence and location of local increases (or decreases) of f, based on all intervals I(all) spanned by any two observations X(j), X(k). The second method approximates the latter approach by using only a subset of I(all) and is therefore computationally much more efficient, but asymptotically equivalent. Omitting the additive correction term Gamma in either method offers another two approaches which are more powerful on small scales and less powerful on large scales, however, not asymptotically minimax optimal anymore. Finally, the block procedure is a compromise between adding Gamma or not, having intermediate power properties. The latter is again asymptotically equivalent to the first and was introduced in Rufibach and Walther (2010).
|Author||Kaspar Rufibach <firstname.lastname@example.org> and Guenther Walther <email@example.com>|
|Date of publication||2015-07-03 08:47:50|
|Maintainer||Kaspar Rufibach <firstname.lastname@example.org>|
|License||GPL (>= 2)|
blocks: Computes number of observations for each block
criticalValuesAll: Compute critical values based on the set of all intervals
criticalValuesApprox: Compute critical values for (1) the original test statistic...
cvModeAll: Critical values for test statistic based on all intervals
cvModeApprox: Critical values for test statistic based on the approximating...
cvModeBlock: Critical values for test statistic based on the block...
lin: Perturbed Uniform Distribution
minimalIntervals: Compute set of minimal intervals
modeHunting: Multiscale analysis of a density on all possible intervals
modeHuntingApprox: Multiscale analysis of a density on the approximating set of...
modeHuntingBlock: Multiscale analysis of a density via block procedure
modehunt-package: Multiscale Analysis for Density Functions
myRound: Round 5 up to the next higher integer
preProcessX: Prepare data vector according to available information on...