coefmatrix: Computation of Coefficients of SBF and SW
Description
This function generates several coefficients such as coefficients of SBF in spherical wavelets (SW),
coefficients of SBF after removing subnet $l$, and coefficients of SW for subnet $l$.Usage
coefmatrix(beta1, fullcov, netlab, l)
Arguments
beta1
coefficients of SBF from previous SBF representation
fullcov
covariance matrix of all observation sites
netlab
vector of labels representing sub-networks
Value
- wcoefcoefficients of SBF in SW
- beta2coefficients of SBF after removing sub-network $l$
- gamma1coefficients of SW for sub-network $l$
- alpha1detailed coefficients of SBF for sub-network $l$
- normnorms of SW for sub-network $l$
Details
The multiresolution analysis based on SBF is derived from the problem of characterizing the loss in an SBF representation
as the number of observations are more larger. This function provides the coefficients of basis functions of multiresolution levels.
For details, see references below.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.