Multiscale Analysis for Density Functions
Computes number of observations for each block
Compute critical values based on the set of all intervals
Compute critical values for (1) the original test statistic with or wi...
Perturbed Uniform Distribution
Compute set of minimal intervals
Multiscale Analysis for Density Functions
Multiscale analysis of a density on all possible intervals
Multiscale analysis of a density on the approximating set of intervals
Multiscale analysis of a density via block procedure
Round 5 up to the next higher integer
Prepare data vector according to available information on support endp...
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).