kerndensp: Closeness of multivariate distribution to elliptical unimodal...
In otrimle: Robust Model-Based Clustering

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2	kerndensp(x,weights=rep(1,nrow(as.matrix(x))), siglist,maxq=qnorm(0.9995), kernn=100)

`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.

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.

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.

Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/

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.

kerndensmeasure, kerndenscluster

  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