artificial.levels {liftLRD} | R Documentation |

## artificial.levels

### Description

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

### Usage

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

### Arguments

`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 |

### Details

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.

### Value

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

### Author(s)

Matt Nunes, Marina Knight

### References

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.

### See Also

### Examples

```
#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
#
```

*liftLRD*version 1.0-9 Index]