crossval_loo {SpatFD}

Leave-One-Out Cross-Validation for Functional Kriging

Description

This function performs leave-one-out cross-validation for functional kriging and cokriging. It systematically leaves out one observation at a time from the dataset, fits the model to the remaining data, and then makes a prediction for the left-out observation. It is used to assess the predictive performance of the functional kriging model.

Usage

crossval_loo(object, plot_show)

Arguments

object

A 'KS_pred' object obtained with function KS_scores_lambdas.

plot_show

A logical value. If TRUE, the function will generate and display a plot of the cross-validation results. If FALSE, no plot will be displayed. Default is True.

Value

An object containing the results of the leave-one-out cross-validation. Includes:

performance_metrics

Summary statistics describing the overall predictive performance, such as mean squared error.

plots

The generation of plots showing the cross-validation results, controlled by the plot_show parameter. If plot_show is TRUE, this will contain the plots; otherwise, it will be empty.

Author(s)

Joan Castro [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).

See Also

recons_fd, KS_scores_lambdas

Examples

# Example code demonstrating how to use the crossval_loo function
library(SpatFD)
library(gstat)

# Load data and coordinates
data(AirQualityBogota)

#s_0 nonsampled location. It could be data.frame or matrix and one or more locations of interest
newcoorden=data.frame(X=seq(93000,105000,len=100),Y=seq(97000,112000,len=100))
#newcoorden=data.frame(X=110000,Y=126000)
#newcoorden=matrix(c(110000.23,109000,109500,130000.81,129000,131000),nrow=3,ncol=2,byrow=TRUE)

# Building the SpatFD object
SFD_PM10 <- SpatFD(PM10, coords = coord[, -1], basis = "Bsplines", 
nbasis = 17,norder=5, lambda = 0.00002, nharm=3)

# Semivariogram models for each spatial random field of scores
modelos <- list(vgm(psill = 2199288.58, "Wav", range = 1484.57, nugget =  0),
                vgm(psill = 62640.74, "Mat", range = 1979.43, nugget = 0,kappa=0.68),
                vgm(psill =37098.25, "Exp", range = 6433.16, nugget =  0))

# Functional kriging. Functional spatial prediction at each location of interest
#method = "lambda"
#Computation of lambda_i
KS_SFD_PM10_l <- KS_scores_lambdas(SFD_PM10, newcoorden ,method = "lambda", 
model = modelos)
# method = "scores"
#Simple kriging of 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)

# Cross Validation 
crossval_loo(KS_SFD_PM10_l)
crossval_loo(KS_SFD_PM10_sc)
crossval_loo(KS_SFD_PM10_both)