geo_fda {geoFourierFDA}

Geostatistical estimates for function-valued data.

Description

geo_fda finds the ordinary kriging estimate for sptial functional data using the model proposed by Giraldo(2011).

Usage

geo_fda(
  m_data,
  m_coord,
  new_coord,
  m,
  n_quad = 20,
  t = seq(from = -pi, to = pi, length.out = 1000)
)

Arguments

m_data

a matrix where each column is a time series in a location

m_coord

a matrix with coordinates (first column is latitude and second column longitude)

new_coord

a vector with a new coordinate (first column is latitude and second longitude)

m

order of the Fourier polynomial

n_quad

a scalar with number of quadrature points. Default value nquad = 20.

t

a vector with points to evaluate from -\pi to \pi. Default t = seq(from = -pi,to = pi,length.out = 1e+3).

Details

geo_fda is similar to model proposed by giraldo2011ordinary. The mais difference is we have used gauss-legendre quadrature to estimate the trace-variogram. Using gauss-legendre qudrature gives estimates with smaller mean square error than the trace-variogram estimates from Giraldo(2011).

For now, we have used Fourier's series to smooth the time series.

Value

a list with three components

curve

estimate curve at t points

lambda

weights in the linear combination in the functional kriging

x

points where the curve was evaluated

References

Giraldo, R., Delicado, P., & Mateu, J. (2011). Ordinary kriging for function-valued spatial data. Environmental and Ecological Statistics, 18(3), 411-426.

Giraldo, R., Mateu, J., & Delicado, P. (2012). geofd: an R package for function-valued geostatistical prediction. Revista Colombiana de Estadística, 35(3), 385-407.

See Also

coef_fourier, fourier_b

Examples

data(canada)

y_hat <- geo_fda(canada$m_data, canada$m_coord, canada$ThePas_coord,
n_quad = 2)