SimulatedSNR9Series: Simulated Wavelet Signals with SNR=9 In WiSEBoot: Wild Scale-Enhanced Bootstrap

Description

A matrix containing simulated signals with noise added such that the signal-to-noise ratio (SNR) is 9. If the signal vector is called Y, and Y is of length 2^J, we have defined the SNR within the J0=j threshold as

SNR=(1/2^J)( (<Y, Y>/(2^j-1)) / (σ^2/(2^J - 2^j -1)))

where σ^2 is the variance of the noise. These series are obtained by adding white noise to the smooth data in `SimulatedSmoothSeries`. Each column contains a wavelet coefficient threshold level and rows contain observations.

Usage

 `1` ```data("SimulatedSNR9Series") ```

Format

The format is:

num [1:1024, 1:9] -0.01879 -0.01635 -0.01096 -0.00814 -0.00423 ...

- attr(*, "dimnames")=List of 2

..\$ : NULL

..\$ : chr [1:9] "J0.0" "J0.1" "J0.2" "J0.3" ...

Details

The columns contain noisy series with signals in different wavelet coefficient threshold levels. Series are available for signal thresholds of J0 in {0, 1, 2, 3, 4, 5, 6, 7, 8}. The rows are the data observations. Thus, each smooth series is of length 2^{10}=1024.

The names of each column indicate the threshold (J0) in the smooth series. For example, the 3rd column, named `J0.2`, has a threshold of J0=2 in the signal, and thus 0-valued wavelet coefficients for all mother wavelet coefficients finer than level 2 in the signal. Notice, the white noise added to the signal creates non-zero coefficients above the threshold.

The original smooth series were generated using `'wd'` and `'wr'` with the `family="DaubLeAsymm"`, `filter.number=8`, `bc="periodic"` options in the `'wavethresh'` package.

References

`wavethresh-package`, `SimulatedSmoothSeries`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```data(SimulatedSNR9Series) ##See if WiSEBoot selects the correct threshold for this data (J0=3) ## R=10 bootstrap samples is not recommended. For demonstration only. bootObj <- WiSEBoot(SimulatedSNR9Series[,4], R=10) bootObj\$MSECriteria ##Look at the noisy data compared to the true smooth data(SimulatedSmoothSeries) plot(seq(1, 2^10), SimulatedSNR9Series[ , 6], main="Threshold of J0=5", col="lightgray", xlab="Time", ylab="Observations", type="l") lines(seq(1, 2^10), SimulatedSmoothSeries[ ,6], col="red", lwd=2) ```

Example output

```      J0plusOne  meanOfMSE
[1,]         9 0.03771718
[2,]         8 0.03492006
[3,]         7 0.02749739
[4,]         6 0.02274555
[5,]         5 0.01907403
[6,]         4 0.01829780
[7,]         3 0.01911155
[8,]         2 0.01875261
[9,]         1 0.01892079
[10,]         0 0.01918460
```

WiSEBoot documentation built on May 2, 2019, 12:35 p.m.