goldenshluger_lepski: Goldenshluger-Lepski Method

In hericks/KDE: Kernel Density Estimation

Description

The Goldenshluger-Lepski method is used to estimate an optimal bandwidth for kernel density estimation from a given set of bandwidths.

Usage

goldenshluger_lepski(
  kernel,
  samples,
  bandwidths = logarithmic_bandwidth_set(1/length(samples), 1, 10),
  kappa = 1.2,
  subdivisions = 1000L
)

Arguments

kernel	S3 object of class Kernel; the kernel to use for the estimator
samples	numeric vector; the observations.
bandwidths	strictly positive numeric vector; the bandwidth set from which the bandwidth with the least estimated risk will be selected.
kappa	numeric scalar greater 1; a tuning parameter.
subdivisions	positive numeric scalar; subdivisions parameter internally passed to integrate_primitive.

Details

The Goldenshluger-Lepski method aims to minimize an upper bound for the mean integrated squared error (MISE) of a kernel density estimator. The MISE is defined as the expectation of the squared L2-Norm of the difference between estimator and (unknown) true density.

This methods works with the popular bias-/variance-decomposition. A double-kernel approach is used for an estimator of the bias term as it still depends on the unknown density.

The estimator used for an upper bound of the variance depends on the tuning parameter kappa. The recommended value for kappa is 1.2.

Subsequently the bandwidth with the minimal associated risk is selected.

Value

The estimated optimal bandwidth contained in the bandwidth set.

Source

Nonparametric Estimation, Comte [2017], ISBN: 978-2-36693-030-6

See Also

kernel_density_estimator for more information about kernel density estimators, pco_method and cross_validation for more automatic bandwidth-selection algorithms.

hericks/KDE documentation built on Aug. 22, 2020, 12:04 a.m.