sbf: Extrapolation with Multi-sale SBF's
In SpherWave: Spherical Wavelets and SW-based Spatially Adaptive Methods

Description Usage Arguments Details Value References See Also Examples

This function performs extrapolation with multi-sale SBF's.

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sbf(obs, latlon, netlab, eta, method, approx=FALSE,
    grid.size=c(50, 100), lambda=NULL, p0=0, latlim=NULL, 
    lonlim=NULL)

`obs`	observations
`latlon`	grid points of observation sites in degree. Latitude is the angular distance in degrees of a point north or south of the Equator. North/South are represented by +/- sign. Longitude is the angular distance in degrees of a point east or west of the Prime (Greenwich) Meridian. East/West are represented by +/- sign.
`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`	specifies starting level for extrapolation. Among resolution levels 1, …, L, resolution levels p0+1, …, L will be included for extrapolation.
`latlim`	range of latitudes in degree
`lonlim`	range of longitudes in degree

This function performs extrapolation with multi-sale SBF's.

An object of class ‘sbf’. 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
`density`	density on observation's locations
`latlim`	range of latitudes in degree
`lonlim`	range of longitudes in degree

Oh, H-S. (1999) Spherical wavelets and their statistical analysis with applications to meteorological data. Ph.D. Thesis, Department of Statistics, Texas A\&M University, College Station.

Li, T-H. (1999) Multiscale representation and analysis of spherical data by spherical wavelets. SIAM Journal on Scientific Computing, 21, 924–953.

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.

swd, swthresh, swr.

### 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)