In Rufibach and Walther (2010) a new multiscale mode hunting procedure is presented that compares the local test statistics with critical values given by blocks. Blocks are collection of intervals on a given grid that contain roughly the same number of original observations.
blocks(n, m0 = 10, fm = 2)\(b \times 2\)--matrix, where \(b\) is the number of blocks and the columns contain the lower and the upper number of observations that form each block.
Number of observations.
Initial parameter that determines the number of observations in one block.
Factor by which \(m\) is increased from block to block.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Guenther Walther, gwalther@stanford.edu,
https://gwalther.su.domains/
In our block procedure, we only consider a subset \(\mathcal{I}_{app}\) of all possible intervals \(\mathcal{I}_{all}\) where
$$\mathcal{I}_{all} = \Bigl\{(j, \ k ) \ : \ 0 \le j < k \le n+1, \ k - j > 1\Bigr\}.$$
This subset \(\mathcal{I}_{app}\) is computed as follows:
Set \(d_1, m_1, f_m > 1\). Then:
\(for \ \ r = 1,\ldots,\#blocks\)
\(d_r := round(d_1 f_m^{(r-1)/2}), \ m_r := m_1 f_m^{r-1}.\)
Include \((j,k)\) in \(\mathcal{I}_{app}\) if
(a) \(j, k \in \{1+i d_r, \ i = 0, 1, \dots \}\) \ \ (we only consider every \(d\)--th observation) and
(b) \(m_r \le k-j-1 \le 2m_r-1\) \ \ (\(\mathcal{I}_{jk}\) contains between \(m_r\) and \(2m_r - 1\) observations)
\(end \ \ for\)
Rufibach, K. and Walther, G. (2010). A general criterion for multiscale inference. J. Comput. Graph. Statist., 19, 175--190.
This function is called by modeHuntingBlock.