Description Usage Format Details References Examples

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.

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

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" ...

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.

`wavethresh-package`

, `SimulatedSmoothSeries`

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)
``` |

```
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
```

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