kerndensp {otrimle}

Closeness of multivariate distribution to elliptical unimodal distribution

Description

Density- and and principal components-based distance between multivariate data and a unimodal elliptical distribution about the data mean, see Hennig and Coretto (2021). For use in kerndenscluster.

Usage

  kerndensp(x,weights=rep(1,nrow(as.matrix(x))), siglist,maxq=qnorm(0.9995),
            kernn=100)

Arguments

x

something that can be coerced into a matrix. Dataset.

weights

non-negative vector. Relative weights of observations (will be standardised to sup up to one internally).

siglist

list with components cov (covariance matrix), center (mean) and n.obs (number of observations).

maxq

positive numeric. One-dimensional densities are evaluated between mean(x)-maxq and mean(x)+maxq.

kernn

integer. Number of points at which the one-dimensional density is evaluated, input parameter n of density. This should be even.

Details

See Hennig and Coretto (2021), Sec. 4.2. kerndensmeasure is run on the principal components of x. The resulting measures are standardised by kmeanfun and ksdfun and then aggregated as mean square of the positive values, see Hennig and Coretto (2021). The PCS is computed by princomp and will always use siglist rather than statistics computed from x.

Value

A list with components cml, cm, pca, stanmeasure, measure.

cml

List of outputs of kerndensmeasure for the principal components.

cm

vector of measure components of kerndensmeasure for the principal components.

stanmeasure

vector of standardised measure components of kerndensmeasure for the principal components.

pca

output of princomp.

measure

Final aggregation result.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

Hennig, C. and P.Coretto (2021). An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture based clustering. To appear in Australian and New Zealand Journal of Statistics, https://arxiv.org/abs/2009.00921.

See Also

kerndensmeasure, kerndenscluster

Examples

  set.seed(124578)
  x <- cbind(runif(20),runif(20))
  siglist <- list(cov=cov(x),center=colMeans(x),n.obs=20) 
  kerndensp(x,siglist=siglist)$measure