sbf                package:SpherWave                R Documentation

_E_x_t_r_a_p_o_l_a_t_i_o_n _w_i_t_h _M_u_l_t_i-_s_a_l_e _S_B_F'_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

     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

_D_e_t_a_i_l_s:

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

_V_a_l_u_e:

     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

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

     'swd', 'swthresh', 'swr'.

_E_x_a_m_p_l_e_s:

     ### 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)

