# Extrapolation with Multi-sale SBF's

### Description

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

### Usage

1 2 3 |

### 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 |

`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 |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
### 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)
``` |