sbf: Extrapolation with Multi-sale SBF's

Description

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

Usage

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

specifies starting level for extrapolation. Among resolution levels $1, \ldots, L$, resolution levels $p0+1, \ldots, L$ will be included for extrapolation.

latlim

range of latitudes in degree

lonlim

range of longitudes in degree

Value

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
density: density on observation's locations
latlim: range of latitudes in degree
lonlim: range of longitudes in degree

Details

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

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.

Examples

Run this code

### 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)

Run the code above in your browser using DataLab