Thresholding of Spherical Wavelet Decomposition (‘swd’) Object

Description

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

Usage

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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

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 p0+1, …, 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

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

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### 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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