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

resolution level

Value

wcoef: coefficients of SBF in SW
beta2: coefficients of SBF after removing sub-network $l$
gamma1: coefficients of SW for sub-network $l$
alpha1: detailed coefficients of SBF for sub-network $l$
norm: norms 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.