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Compact-support Epanechnikov target

Source: R/gmm_target_constructors.R
epanechnikov_target.Rd

The canonical compact-support target: a product of one-dimensional Epanechnikov densities \(K(u) = \tfrac{3}{4}(1 - u^2)\,\mathbf{1}_{|u| \le 1}\), rescaled to [center - half_width, center + half_width] in each coordinate. No mixture of full-support Gaussians can have compact support, so this target is the clean case where regime (iii) is the only viable fitting route. It declares its support, which makes fit_kld_em() (and fit_proxymix() with regime = "kld") select a support-matched uniform proposal automatically instead of the default multivariate-t, which would place importance mass where the log-density is -Inf.

Usage

epanechnikov_target(
  n_dim = 1L,
  center = 0,
  half_width = 1,
  with_samples = FALSE,
  n = 2000L,
  seed = 1L
)

Arguments

n_dim

Ambient dimension p.

center

Length-1 (recycled) or length-p numeric centre per coordinate.

half_width

Length-1 (recycled) or length-p positive numeric half-width per coordinate.

with_samples

If TRUE, attach n exact samples drawn by the Devroye (1986) three-uniform method. Default FALSE.

n

Number of samples to attach when with_samples = TRUE.

seed

Optional integer seed used when drawing the samples.

Value

A gmm_target in dimension n_dim with a declared compact support.

See also

Other targets: banana_target(), donut_target(), gmm_target_from_samples(), maxent_target(), mixture_target()

Examples

e <- epanechnikov_target()
e
#> <gmm_target>: "epanechnikov" in p = 1 dimensions
#>   log_density : supplied
#>   samples     : <absent>
#>   normalised  : TRUE
#>   log Z(f)    : 0
#>   support     : [-1, 1]
e@log_density(matrix(c(0, 0.5, 1.5), ncol = 1L)) # finite, finite, -Inf
#> [1] -0.2876821 -0.5753641       -Inf