sobolnp {sobolnp}

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)

Arguments

Y

Response continuous variable

X

Matrix of independent variables

bandwidth

If bandwidth.compute = TRUE, it sets the starting bandwidth to find the bootstrap bandwidth. If NULL the least-square cross-validation bandwidth is used. If bandwidth.compute = FALSE, it will use the values provided fixed over all the simulation. 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.

Value

A list of class sobolnp with the following elements:

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

References

Solís, Maikol. "Nonparametric estimation of the first order Sobol indices with bootstrap bandwidth." arXiv preprint arXiv:1803.03333 (2018).

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)