# Thresholding of Spherical Wavelet Decomposition (‘swd’) Object

### Description

This function performs various ways to threshold a ‘swd’ class object.

### Usage

1 2 |

### Arguments

`swd` |
an object of class ‘swd’ |

`policy` |
threshold technique. At present the possible policies are ‘"universal"’, ‘"probability"’, ‘"fdr"’, ‘"Lorentz"’ and ‘"sure"’. |

`by.level` |
If FALSE, then perform a global threshold. If TRUE, a thresholding value is computed and applied separately to each resolution level. |

`type` |
the type of thresholding. This can be ‘"hard"’, ‘"soft"’ or ‘"Lorentz"’. |

`nthresh` |
the number of resolution levels to be thresholded in the decomposition |

`value` |
the user supplied threshold represented by quantile level for ‘"probability"’ policy |

`Q` |
parameter for the false discovery rate of ‘"fdr"’ policy |

### Details

This function thresholds or shrinks details stored in a ‘swd’ object and returns the thresholded details in a modified ‘swd’ object. For level-dependent thresholding, ‘"universal"’, ‘"Lorentz"’ and ‘"fdr"’ are provided. Only hard type thresholding is proper for ‘"probability"’ thresholding. Also note that only soft type thresholding is proper for ‘"sure"’ thresholding.

### Value

An object of class ‘swd’. This object is a list with the following components.

`obs` |
observations |

`latlon` |
grid points of observation sites in degree |

`netlab` |
vector of labels representing sub-networks |

`eta` |
bandwidth parameters for Poisson kernel |

`method` |
extrapolation methods, ‘"ls"’ or ‘"pls"’ |

`approx` |
if TRUE, approximation is used. |

`grid.size` |
grid size (latitude, longitude) of extrapolation site |

`lambda` |
smoothing parameter for penalized least squares method |

`p0` |
starting level for extrapolation. Resolution levels |

`gridlon` |
longitudes of extrapolation sites in degree |

`gridlat` |
latitudes of extrapolation sites in degree |

`nlevels` |
the number of multi-resolution levels |

`coeff` |
interpolation coefficients |

`field` |
extrapolation on grid.size |

`density1` |
density of SBF |

`latlim` |
range of latitudes in degree |

`lonlim` |
range of longitudes in degree |

`global` |
List of successively smoothed data |

`density` |
density of SW coefficients |

`detail` |
List of details at different resolution levels |

`swcoeff` |
spherical wavelet coefficients |

`thresh.info` |
thresholding information and ranges of local components before thresholding |

### References

Oh, H-S. and Li, T-H. (2004) Estimation of global temperature fields from scattered observations by
a spherical-wavelet-based spatially adaptive method. *Journal of the Royal Statistical Society
Ser.* B, **66**, 221–238.

### See Also

`sbf`

, `swd`

, `swr`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
### Observations of year 1967
#data(temperature)
#names(temperature)
# Temperatures on 939 weather stations of year 1967
#temp67 <- temperature$obs[temperature$year == 1967]
# Locations of 939 weather stations
#latlon <- temperature$latlon[temperature$year == 1967, ]
### Network design by BUD
#data(netlab)
### Bandwidth for Poisson kernel
#eta <- c(0.961, 0.923, 0.852, 0.723, 0.506)
### SBF representation of the observations by pls
#out.pls <- sbf(obs=temp67, latlon=latlon, netlab=netlab, eta=eta,
# method="pls", grid.size=c(50, 100), lambda=0.89)
### Decomposition
#out.dpls <- swd(out.pls)
### Thresholding
#out.univ <- swthresh(out.dpls, policy="universal", by.level=TRUE,
# type="hard", nthresh=4)
``` |

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