SpherWave (version 1.2.1)

swthresh: Thresholding of Spherical Wavelet Decomposition (`swd') Object

Description

This function performs various ways to threshold a `swd' class object.

Usage

swthresh(swd, policy, by.level, type, nthresh, value = 0.1, 
Q = 0.05)

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

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 $p0+1, \ldots, L$ is used for extrapolation.
• 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

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.

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

### 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)