R: Data analytic wavelet thresholding routine

TOthreshda1 {wavethresh} | R Documentation

## Data analytic wavelet thresholding routine

### Description

This function might be better called using the regular `threshold` function using the `op1` policy.

Corresponds to the wavelet thresholding routine developed by Ogden and Parzen (1994) Data dependent wavelet thresholding in nonparametric regression with change-point applications. Tech Rep 176, University of South Carolina, Department of Statistics.

### Usage

    TOthreshda1(ywd, alpha = 0.05, verbose = FALSE, return.threshold = FALSE)

### Arguments

`ywd` | The `wd.object` that you wish to threshold.
`alpha` | The smoothing parameter which is a p-value
`verbose` | Whether messages get printed
`return.threshold` | If TRUE then the threshold value gets returned rather than the actual thresholded object

### Details

The TOthreshda1 method operates by testing the max of each set of squared wavelet coefficients to see if it behaves as the nth order statistic of a set of independent chi^2(1) r.v.'s. If not, it is removed, and the max of the remaining subset is tested, continuing in this fashion until the max of the subset is judged not to be significant.

In this situation, the level of the hypothesis tests, alpha, has default value 0.05. Note that the choice of alpha controls the smoothness of the resulting wavelet estimator – in general, a relatively large alpha makes it easier to include coefficients, resulting in a more wiggly estimate; a smaller alpha will make it more difficult to include coefficients, yielding smoother estimates.

### Value

Returns the threshold value if `return.threshold==TRUE` otherwise returns the shrunk set of wavelet coefficients.

### Author(s)

Todd Ogden

### See Also

`threshold`,`TOthreshda2`, `wd`

[Package wavethresh version 4.6.8 Index]