# 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

1 | ```
hardThresholding(xdata, delta, verbose = FALSE, varName = NULL, wavFilter="s8")
``` |

### Arguments

`xdata` |
The matrix of |

`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

1 2 3 | ```
data(toyRegFD)
x <- toyRegFD$FDlist[[1]]
newDesignMatrix <- hardThresholding(xdata=x, verbose=TRUE)
``` |