Extrapolation with Multi-sale SBF's

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Description

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

Usage

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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) 

Arguments

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

Details

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

Value

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

References

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.

See Also

swd, swthresh, 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)

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