COKS_scores_lambdas {SpatFD}

Functional cokriging

Description

Linear Spatial functional prediction. Two predictors are possible: scores or lambda.

Usage

COKS_scores_lambdas(SFD, newcoords, model, method = "scores", fill.all=TRUE)

Arguments

SFD

object of class 'SpatFD'.

newcoords

The N × 2 matrix or data.frame with the spatial coordinates corresponding to the N prediction locations.

model

The linear model of coregionalization of all functional variable scores. A variogram model. A variogramModel object. See gstat package.

method

Prediction method: "scores"

fill.all

gstat function parameter. If there are more than 1 score vector and not all models or a valid and complete linear model of coregionalization is given, fill all of the direct and cross variogram model with the only model given.

Details

Each functional variable is represented in terms of its functional principal components \chi_{\bm s_i}(t)=\bm \xi^T(t)\bm f_{\bm s_i},\;i=1,...,n where \bm f_{\bm s_i}=\left(f_{\bm s_i}^1,...,f_{\bm s_i}^K\right)^T

The goal is the prediction of a spatial functional variable of \chi^r_{\bm s_0}(t)\;1\leq r\leq P at the unsampled site \bm s_0 based on P spatial functional variables. The method performs cokriging directly on the scores chosen for all functional variables involved.

\left(\bm f_{\bm s}^{11},...,f_{\bm s}^{1K_1},...,f_{\bm s}^{P1},...,f_{\bm s}^{PK_P}\right)

Scores predictions are used to build the cokriging functional predictor.

Value

Returns a 'COKS_pred' object with functional cokriging

Author(s)

Valeria Bejarano <[e-mail]>

References

Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Multivariate functional random fields: prediction and optimal sampling. Stochastic Environmental Research and Risk Assessment, 31, pages53–70 (2017).

Bohorquez M.; Giraldo R. and Mateu J. Spatial prediction and optimal sampling of functional data in Geostatistical Functional Data Analysis: Theory and Methods (2021). John Wiley Sons, Chichester, UK. ISBN: 978-1-119-38784-8. https://www.wiley.com/en-us/Geostatistical+Functional+Data+Analysis-p-9781119387848.

See Also

SpatFD,summary.COKS_pred

Examples

data(COKMexico)
SFD_PM10_NO2 <- SpatFD(Mex_PM10, coords = coord_PM10, basis = "Fourier", 
nbasis = 21, lambda = 0.000001, nharm = 2)
SFD_PM10_NO2 <- SpatFD(NO2, coords = coord_NO2, basis = "Fourier", 
nbasis = 27, lambda = 0.000001, nharm = 2,
                      add = SFD_PM10_NO2)
model1 <- gstat::vgm(647677.1,"Gau",23317.05)
model1 <- gstat::vgm(127633,"Wav",9408.63, add.to = model1)
newcoords <- data.frame(x = 509926,y = 2179149)
COKS_scores_lambdas(SFD_PM10_NO2,newcoords,model1)