Description Usage Arguments Details Value Author(s) References See Also Examples

This function splits the coefficients into levels according to either (i) increasing quantiles of the removed interval lengths or (ii) dyadic splitting relative to a fixed lowest scale

1 | ```
artificial.levels(y, rem, time, tail = TRUE, type = 1)
``` |

`y` |
a vector of the removed interval lengths (in the order of removelist). |

`rem` |
vector of indices of the removed points (from the output of the forward transform). |

`time` |
vector of observed times for the decomposed signal. |

`tail` |
a boolean variable indicating whether coarse levels with a small number of detail coefficients (less than 10 coefficients) should be combined. |

`type` |
an integer indicating which type of artificial levels to compute. If |

The function computes the so-called artificial levels of a set of removed integrals and corresponding detail coefficients, to mimic the dyadic level splitting in a classical
wavelet framework. Details on the "usual" quantile-based splitting can be found in `artlev`

. If `type==2`

or `type==3`

, the artificial levels are
defined by intervals of the form [a0 2^j,a0 2^(j-1) ) as described in Jansen et al. (2009), with a0 = 0.5 for `type==2`

and set to the minimum sampling interval for
`type==3`

. The amalgamation of coarser artificial levels prevents variable energies at coarser scales affecting the predicted relationship between the wavelet scales
and their corresponding energies.

`p` |
a list of the grouped indices of removelist (in decreasing group size) indicating thresholding groups. |

Matt Nunes, Marina Knight

Jansen, M, Nason, G. P. and Silverman, B. W. (2009) Multiscale methods for data on graphs and irregular
multidimensional situations. *J. Roy. Stat. Soc. B* **71**, Part 1, 97–125.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
#create test signal data
#
library(adlift)
x<-runif(100)
y<-make.signal2("blocks",x=x)
#
#perform forward transform...
#
out<-fwtnp(x,y,LocalPred=AdaptNeigh,neighbours=2)
#
al<-artificial.levels(out$lengthsremove,out$removelist, x, type = 1)
#
#
# the indices of removelist split into levels:
al
#
``` |

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