| Title: | Kriging Method for Spatial Functional Data |
| Version: | 0.1.1 |
| Maintainer: | Gilberto Sassi <sassi.pereira.gilberto@gmail.com> |
| Description: | A Kriging method for functional datasets with spatial dependency. This functional Kriging method avoids the need to estimate the trace-variogram, and the curve is estimated by minimizing a quadratic form. The curves in the functional dataset are smoothed using Fourier series. The functional Kriging of this package is a modification of the method proposed by Giraldo (2011) <doi:10.1007/s10651-010-0143-y>. |
| Imports: | numDeriv, stats, Rcpp |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.2 |
| URL: | https://github.com/gilberto-sassi/geoFKF |
| BugReports: | https://github.com/gilberto-sassi/geoFKF/issues |
| LinkingTo: | Rcpp, RcppArmadillo |
| NeedsCompilation: | yes |
| Packaged: | 2022-08-12 19:06:56 UTC; gilberto |
| Author: | Gilberto Sassi [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2022-08-12 19:50:02 UTC |
Computing coefficients Fourier.
Description
This function computes minimum square estimates for Fourier coefficients.
Usage
coef_fourier(f, m)
Arguments
f |
A time series to be smoothed. |
m |
Order of the Fourier polynomial. Default value is computed using the Sturge's rule. |
Value
A vector with the fourier coefficients.
Examples
x <- seq(from = -pi, to = pi, by = 0.01)
y <- x^2 + rnorm(length(x), sd = 0.1)
v_coef <- coef_fourier(y)
Temperature datasets from Canada.
Description
Temperature time series from 35 weather stations from Canada. This dataset
is a classic one and was used in famous package fda. We have made a few
changes in this dataset.
Usage
data("datasetCanada")
Format
A list with two entries: m_cood and m_data.
m_coorda
tibblewith latitude, logitude and the name of stations.- m_data
a
tibblewhere each column is the time series from a weather station.
Source
the CanadianWeather dataset from the R package
fda.
Smoothed curve in Fourier Series.
Description
This function computes the smoothed curve using Fourier coefficients.
Usage
fourier_b(coef, x)
Arguments
coef |
Fourier coefficients. |
x |
a time series to evaluate the smoothed curve. |
Value
a time series with the smoothed curve.
Examples
v_coef <- rnorm(23)
fourier_b(v_coef)
Kriging method for Spatial Functional Data.
Description
geo_fkf implements the kriging method for spatial functional datasets.
Usage
geo_fkf(m_data, m_coord, new_loc, p, t = seq(from = -pi, to = pi, by = 0.01))
Arguments
m_data |
a tibble where each column or variable is data from a station |
m_coord |
a tibble with two columns: latitude and longitude |
new_loc |
a tible with one observation, where the columns or variables are latitude and longitude |
p |
order in the Fourier Polynomial |
t |
a time series with values belonging to |
Value
a list with three entries: estimates, Theta and
cov_params
- estimates
the estimate curve
- Theta
weights (matrices) of the linear combination
- cov_params
estimate
\sigma^2,\phiand\rho
Examples
data("datasetCanada")
m_data <- as.matrix(datasetCanada$m_data)
m_coord <- as.matrix(datasetCanada$m_coord[, 1:2])
pos <- sample.int(nrow(m_coord), 1)
log_pos <- !(seq_len(nrow(m_coord)) %in% pos)
new_loc <- m_coord[pos, ]
m_coord <- m_coord[log_pos, ]
m_data <- m_data[, log_pos]
geo_fkf(m_data, m_coord, new_loc)
Log likelihood function for multivariate normal with spatial dependency.
Description
Log likelihood function for multivariate normal with spatial dependency.
Arguments
mCoef |
coefficient matrix. Each column is the coefficient from a curve; |
mDist |
distance matris; |
s2 |
variance from the covariance model; |
phi |
variance from the covariance model; |
rho |
variance from the covariance model; |
Maximum likelihood estimate for \sigma^2, \phi and \rho.
Description
This function maximum likelihood estimate for \sigma^2, \phi
and \rho in the random field model for the covariance.
Usage
log_lik_rf(m_coef, m_coord)
Arguments
m_coef |
Matrix where each column is an observed vector |
m_coord |
Matrix where each observation contains the latitude and longitude |
Value
Return a list with
- par
A vector with the estimates of
\sigma^2,\phiand\rho.- m_cov
A matrix of covariances of the estimates.
Examples
data("datasetCanada")
m_data <- as.matrix(datasetCanada$m_data)
m_coord <- as.matrix(datasetCanada$m_coord[, 1:2])
p <- ceiling(1 + log2(nrow(m_data)))
m_coef <- sapply(seq_len(nrow(m_coord)), function(i) {
coef_fourier(m_data[, i], p)
})
log_lik_rf(m_coef, m_coord)