Package {sobolnp}

Type: Package
Title: Nonparametric Sobol Estimator with Bootstrap Bandwidth
Version: 0.2.0
Description: Algorithm to estimate the Sobol indices using a non-parametric fit of the regression curve. The bandwidth is estimated using bootstrap to reduce the finite-sample bias. The package is based on the paper Solís, M. (2021) <doi:10.1080/03610918.2019.1655575>.
License: MIT + file LICENSE
URL: https://github.com/maikol-solis/sobolnp/
BugReports: https://github.com/maikol-solis/sobolnp/issues
Imports: np, parallel, pbmcapply
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
Encoding: UTF-8
Config/roxygen2/version: 8.1.1
NeedsCompilation: no
Packaged: 2026-11-09 19:00:15 UTC; maikol
Author: Maikol Solís [aut, cre]
Maintainer: Maikol Solís <maikol.solis@ucr.ac.cr>
Repository: CRAN
Date/Publication: 2026-11-09 19:50:02 UTC

Plot method for objects sobolnp

Description

Bar plot of the first order Sobol indices estimated by sobolnp, with the cross-validation and the bootstrap bandwidth side by side for each variable.

Usage

## S3 method for class 'sobolnp'
plot(
  x,
  ylim = NULL,
  xlab = "Variables",
  ylab = "First order Sobol indices",
  col = c("#0072B2", "#E69F00"),
  legend.pos = "topright",
  ...
)

Arguments

x

an object of class sobolnp.

ylim

limits of the y axis. By default from 0 to the larger of 1 and the largest estimated index.

xlab, ylab

axis labels.

col

colors for the cross-validation and bootstrap bars.

legend.pos

position of the legend, passed to legend. Use NULL to omit it.

...

further graphical arguments passed to barplot.

Value

The object x, invisibly. Called for its side effect of drawing a plot.

Examples


ishigami.fun <- function(X) {
A <- 7
B <- 0.1
sin(X[, 1]) + A * sin(X[, 2])^2 + B * X[, 3]^4 * sin(X[, 1])
}

X <- matrix(runif(3*100, -pi, pi), ncol = 3)
Y <- ishigami.fun(X)

estimation <- sobolnp(Y = Y, X = X, nboot = 5)

plot(estimation)

Print method for objects sobolnp

Description

Print method for objects sobolnp

Usage

## S3 method for class 'sobolnp'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

an object of class sobolnp.

digits

minimal number of significant digits, see print.default.

...

further arguments passed to print.default.

Value

The object x, invisibly. Called for its side effect of printing the estimated indices and bandwidths.

Examples


ishigami.fun <- function(X) {
A <- 7
B <- 0.1
sin(X[, 1]) + A * sin(X[, 2])^2 + B * X[, 3]^4 * sin(X[, 1])
}

X <- matrix(runif(3*100, -pi, pi), ncol = 3)
Y <- ishigami.fun(X)

estimation <- sobolnp(Y = Y, X = X, nboot = 5)

print(estimation)

Nonparametric Sobol Estimator with Bootstrap Bandwidth

Description

Algorithm to estimate the Sobol indices using a non-parametric fit of the regression curve. The bandwidth is estimated using bootstrap to reduce the finite-sample bias.

Usage

sobolnp(
  Y,
  X,
  bandwidth = NULL,
  bandwidth.compute = TRUE,
  bootstrap = TRUE,
  nboot = 100,
  ckerorder = 2,
  mc.cores = 1,
  verbose = TRUE
)

Arguments

Y

Response continuous variable

X

Numeric matrix or data frame of independent variables, with one row per element of Y. Unnamed columns are labelled X1, ..., Xp.

bandwidth

NULL or a positive numeric vector of length 1 or ncol(X) (one bandwidth per variable). If bandwidth.compute = TRUE, it sets the starting value of the least-squares cross-validation search; if NULL np chooses the starting values. If bandwidth.compute = FALSE, the bandwidths are used as given and must be supplied. Defaults to NULL.

bandwidth.compute

Logical value. Indicates if the bandwidth should be estimated or not. Defaults to TRUE.

bootstrap

Logical value. Indicates if the estimation should be with bootstrap or not. Defaults to TRUE.

nboot

Number of bootstrap samples taken for the method. Ignored if 'bootstrap = FALSE'. Defaults to 100.

ckerorder

Numeric value specifying kernel order (should be one of (2,4,6,8)). Defaults to 2.

mc.cores

Number of cores used. Defaults to 1.

verbose

Logical value. If TRUE (default), report progress messages and progress bars.

Details

For each input X_i, the regression curve E[Y | X_i] is estimated by kernel regression with a least-squares cross-validation (CV) bandwidth, and S is the variance of the fitted curve divided by the variance of Y.

With bootstrap = TRUE, the residuals of the CV fit are standardized with a kernel estimate of their scale and resampled to build nboot bootstrap responses. For a bandwidth h, the bootstrap curves give a bias-corrected curve 2 \hat m_{CV} - \bar m^*_h and a bootstrap index. The bootstrap bandwidth bwsboot minimizes the mean squared distance between the bootstrap indices and S, searching between bws / 1000 and bws, and Sboot is the mean bootstrap index at that bandwidth.

Value

A list of class sobolnp with the following elements:

call

The matched call.

num.obs, num.var

Number of observations and of input variables.

S

First order Sobol indices estimated with nonparametric regression and a cross-validation bandwidth

bws

Bandwidth estimated with cross-validation

Sboot

First order Sobol indices estimated with nonparametric regression and a bootstrap bandwidth

bwsboot

Bandwidth estimated with bootstrap

Sboot and bwsboot are NULL when bootstrap = FALSE.

References

Solís, M. (2021). Non-parametric estimation of the first-order Sobol indices with bootstrap bandwidth. Communications in Statistics - Simulation and Computation, 50(9), 2497-2512. doi:10.1080/03610918.2019.1655575

Examples

ishigami.fun <- function(X) {
A <- 7
B <- 0.1
sin(X[, 1]) + A * sin(X[, 2])^2 + B * X[, 3]^4 * sin(X[, 1])
}

X <- matrix(runif(3*100, -pi, pi), ncol = 3)
Y <- ishigami.fun(X)

estimation <- sobolnp(Y = Y, X = X, nboot = 5)