glober.2d {glober}

Estimation of functions with two input variables

Description

This function implements the method described in Savino, M and Levy-Leduc, C (2023) for estimating functions in the two-dimensional setting with observations which are assumed to satisfy a nonparametric regression model. The observation points belong to a compact set of \mathbb{R}^2.

Usage

glober.2d(x, y, xpred, ord, parallel = FALSE, nb.Cores = 1)

Arguments

x

matrix of two columns containing the values of the input variables.

y

vector containing the corresponding response variable associated to the input values \texttt{x}.

xpred

matrix of one column or vector containing the input variables for which f has to be estimated.

ord

order of the B-spline basis used in the regression model. Default is 3 (quadratic B-splines).

parallel

logical, if TRUE then a parallelized version of the code is used. Default is FALSE.

nb.Cores

numerical, number of cores used for parallelization, if parallel is set to TRUE.

Value

festimated

estimation of f at \texttt{xpred}.

knotSelec

list of selected knots for each dimension used in the definition of the B-splines.

rss

residual sum-of-squares (RSS) of the model.

rsq

R-squared of the model, calculated as 1 - \frac{RSS}{TSS} where TSS is the total sum-of-squares of the model.

Examples

# --- Loading values of x --- #
data('x_2D')
# --- Loading values of the corresponding y --- #
data('y_2D')
# --- Loading values of xpred --- #
data('xpred_2D')

# --- Estimation of f at xpred --- #
glober.2d(x = x_2D, y = y_2D, xpred = xpred_2D, ord = 3, parallel = FALSE)


# --- Parallel computing --- #
glober.2d(x = x_2D, y = y_2D, xpred = xpred_2D, ord = 3, parallel = TRUE, nb.Cores = 2)