find_bws: Estimate bandwidths based on local Gaussian likelihood

In LAJordanger/localgaussSpec: Local Gaussian Spectral Analysis

Estimate bandwidths based on local Gaussian likelihood

Description

This internal function can be used to estimate bandwidths based on the local Gaussian likelihood for the approach based on the one-free parameter bivariate Gaussian distribution.

Usage

find_bws(
  data,
  .kernel = c("normal", "uniform"),
  use_boundaries = TRUE,
  boundary_percentiles = c(0.1, 0.9),
  tol = 1e-04
)

Arguments

data	A matrix containing the multivariate observations, one observation in each row. Note that the marginals of these observations must be normalised in order for the assumptions of this code to be satisfied.
.kernel	Specification of the kernel to use, either normal or uniform, with default being the normal one if none is selected. Note: The uniform-kernel takes much longer to compute (a factor of ten when used on a small sample of size $n=200$).
use_boundaries	Logic value, default TRUE, that decides whether or not the bandwidths will be selected within the restrictions given by the argument boundary_percentiles
boundary_percentiles	A vector specifying two percentiles, default c(0.1, 0.9), that will be used on the range of the individual margins in order to ensure that the returned bandwidths are within a "reasonable" range. This argument will be ignored when use_boundaries are given as FALSE.
tol	Convergence tolerance, default value 1e-04. The iteration is terminated when the absolute difference in function value between successive iteration is below tol.

Details

The defaults for this function has been selected after an investigation of how different settings affected the final values, with an emphasis on getting "good enough" values within a shortest possible computational time. Keep in mind that the data must have normalised marginals.

Value

The result of this function is a matrix that for each bivariate combination from the points given in data will return the bandwidths obtained when the function link{find_rho} has been optimised with regard to the selected bivariate subset of the data. In addition to the bandwidths, there will also be a convergence-column that should contain 0 if the numerical combination of the bandwidths succeeded without any problems.

Note

The results based on the one-free parameter bivariate Gaussian distributions can differ quite a bit from the results based on the five-free parameter bivariate Gaussian distributions. It is thus not necessarily reasonable to use a bandwidth based on the one-free parameter for the five-free parameter.

The authors opinion is that the local Gaussian correlation extracted from the one-free parameter bivariate Gaussian density function is a complete waste of computational resources. Do not use it! Use the local Gaussian correlation based on the five-free parameter approach instead.

LAJordanger/localgaussSpec documentation built on May 6, 2023, 4:31 a.m.