KS_scores_lambdas {SpatFD}

Functional Kriging

Description

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

Usage

KS_scores_lambdas(SFD, newcoords, model, method = "lambda", name = NULL, fill.all = NULL)

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 scores variogram model. A variogramModel object. See gstat package.

method

Prediction method: "lambda" or "scores". By default "lambda". See details.

name

The variable to predict in SpatFD object. By default, the predictions is performed for the first variable in the SpatFD object.

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

"lambda" option corresponds to the predictor \breve{\chi}_{\bm s_0}(t), given by

\breve{\chi}_{\bm s_0}(t)=\sum\limits_{i=1}^{n}\lambda_i\chi_{\bm s_i}(t)

and weigths are found such that minimize \left\|\bm\chi_{\bm s_0}(t)-\breve{\chi}_{\bm s_0}(t)\right\|^2.

"scores" method performs kriging or cokriging directly on the scores and predictions are used to build the functional prediction

It is used simple cokriging to predict the vector \bm f(\bm s_0)=\left(f_1(\bm s_0),...,f_K(\bm s_0)\right)^T at the unsampled location \bm s_0. The predictor is f^*(\bm s_0), so the prediction of the curve \chi_{\bm s_0}(t) is \chi^*_{\bm s_0}(t)=\bm \xi^T(t)\bm f^*(\bm s_0),\;\;\;\;\;\;i=1,...,n.

Value

Returns a 'KS_pred' object with functional kriging: weights (lambda) using the first method and kriging score predictions using the second method in Bohorquez, M., Giraldo, R., & Mateu, J. (2016).

Author(s)

Diego Sandoval [e-mail] & Angie Villamil [e-mail].

References

Bohorquez, M., Giraldo, R., & Mateu, J. (2016). Optimal sampling for spatial prediction of functional data. Statistical Methods & Applications, 25(1), 39-54.

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.KS_pred

Examples

library(gstat)
data(AirQualityBogota)

newcoorden=data.frame(X=110000,Y=125000)

# Recibir los datos, suavizarlos y ACP
SFD_PM10 <- SpatFD(PM10, coords = coord[,2:3], basis = "Bsplines",
nbasis = 17,norder=5, lambda = 0.00002, nharm=3)

#Variogram model for each component
modelos <- list(vgm(psill = 2634000, "Exp", range = 2103.25, nugget =  0),
                vgm(psill = 101494.96, "Exp", range = 1484.57, nugget = 0),
                vgm(psill =53673, "Exp", range = 42406, nugget =  0))

#Genera los scores y los lambdas para predecir en nuevas coordenadas

#method = "lambda"
KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda",
model = modelos)
class(KS_SFD_PM10_l)

#method = "scores"
KS_SFD_PM10_sc <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "scores",
model = modelos)

#method = "both"
KS_SFD_PM10_both <- KS_scores_lambdas(SFD_PM10, newcoorden, method = "both",
model = modelos)