Wavelets hard-thresholding rule for independents processes

Description

This function projects n indepedent processes on a common wavelet basis and shrinks to zero the n coefficients whose \ell_2-norm is lower than a threshold.

Usage

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hardThresholding(xdata, delta, verbose = FALSE, varName = NULL, wavFilter="s8")

Arguments

xdata

The matrix of n independent curves of dimension N=2^J, where J is the number of maximum wavelet level.

delta

The desired threshold. If missing, an automatic threshold is computed.

verbose

Should the details be printed.

varName

The name of the current functional variable.

wavFilter

A character string denoting the filter type. Supported types include:

EXTREMAL PHASE (daublet): ‘haar’, ‘d2’, ‘d4’, ‘d6’, ‘d8’, ‘d10’, ‘d12’, ‘d14’, ‘d16’, ‘d18’, ‘d20’

LEAST ASYMMETRIC (symmlet): ‘s2’, ‘s4’, ‘s6’, ‘s8’, ‘s10’, ‘s12’, ‘s14’, ‘s16’, ‘s18’, ‘s20’

BEST LOCALIZED: ‘l2’, ‘l4’, ‘l6’, ‘l14’, ‘l18’, ‘l20’

COIFLET: ‘c6’, ‘c12’, ‘c18’, ‘c24’, ‘c30’

Default: ‘s8’.

Value

A list with two components

mht.names

The names of the common wavelet basis after thresholding the coefficients.

estimatedDesign

The new design matrix after thresholding.

Author(s)

Baptiste Gregorutti

References

Gregorutti, B., Michel, B. and Saint Pierre, P. (2015). Grouped variable importance with random forests and application to multiple functional data analysis, Computational Statistics and Data Analysis 90, 15-35.

See Also

fpca

Examples

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  data(toyRegFD)
  x <- toyRegFD$FDlist[[1]]
  newDesignMatrix <- hardThresholding(xdata=x, verbose=TRUE)