QLMDe_stepK: Forward Selection of the Number of Components K

In QuantileGH: Quantile Least Mahalanobis Distance Estimator for Tukey g-&-h Mixture

Forward Selection of the Number of Components K

Description

To compare gh-parsimonious models of Tukey g-&-h mixtures with different number of components K (up to a user-specified K_\text{max}) and select the optimal number of components.

Usage

QLMDe_stepK(
  x,
  distname = c("GH", "norm"),
  data.name = deparse1(substitute(x)),
  Kmax = 3L,
  test = c("BIC", "AIC"),
  direction = c("forward", "backward"),
  ...
)

Arguments

x	numeric vector, observations
distname, data.name	character scalars, see parameters of the same names in function QLMDe()
Kmax	integer scalar K_\text{max}, maximum number of components to be considered. Default 3L
test	character scalar, criterion to be used, either Akaike's information criterion AIC, or Bayesian information criterion BIC (default).
direction	character scalar, direct of selection in function step_fmx(), either 'forward' (default) or 'backward'
...	additional parameters

Details

Function QLMDe_stepK() compares the gh-parsimonious models with different number of components K, and selects the optimal number of components using BIC (default) or AIC.

The forward selection starts with finding the gh-parsimonious model (via function step_fmx()) at K = 1. Let the current number of component be K^c. We compare the gh-parsimonious models of K^c+1 and K^c component, respectively, using BIC or AIC. If K^c is preferred, then the forward selection is stopped, and K^c is considered the optimal number of components. If K^c+1 is preferred, then the forward selection is stopped if K^c+1=K_{max}, otherwise update K^c with K_c+1 and repeat the previous steps.

Value

Function QLMDe_stepK() returns an object of S3 class 'stepK', which is a list of selected models (in reversed order) with attribute(s) 'direction' and 'test'.

Examples

data(bmi, package = 'mixsmsn')
hist(x <- bmi[[1L]])
QLMDe_stepK(x, distname = 'GH', Kmax = 2L)

QuantileGH documentation built on April 3, 2025, 8:35 p.m.