ssMRCD: Spatially Smoothed MRCD Estimator

Description

The ssMRCD function calculates the spatially smoothed MRCD estimator from Puchhammer and Filzmoser (2023).

Usage

ssMRCD(
  x,
  groups = NULL,
  weights,
  lambda,
  TM = NULL,
  alpha = 0.75,
  maxcond = 50,
  maxcsteps = 200,
  n_initialhsets = NULL
)

Value

An object of class "ssMRCD" containing the following elements:

`MRCDcov`	List of ssMRCD-covariance matrices sorted by neighborhood.

`MRCDicov`	List of inverse ssMRCD-covariance matrices sorted by neighborhood.

`MRCDmu`	List of ssMRCD-mean vectors sorted by neighborhood.

`mX`	List of data matrices sorted by neighborhood.

`N`	Number of neighborhoods.

`mT`	Target matrix.

`rho`	Vector of regularization values sorted by neighborhood.

`alpha`	Scalar what percentage of observations should be used.

`h`	Vector of how many observations are used per neighborhood, sorted.

`numiter`	The number of iterations for the best initial h-set combination.

`c_alpha`	Consistency factor for normality.

`weights`	The weighting matrix.

`lambda`	Smoothing factor.

`obj_fun_values`	A matrix with objective function values for all initial h-set combinations (rows) and iterations (columns).

`best6pack`	initial h-set combinations with best objective function value after c-step iterations.
`Kcov`	returns MRCD-estimates without smoothing.

Arguments

x: a list of matrices containing the observations per neighborhood sorted which can be obtained by the function restructure_as_list, or matrix or data frame containing data. If matrix or data.frame, group vector has to be given.
groups: vector of neighborhood assignments
weights: weighting matrix, symmetrical, rows sum up to one and diagonals need to be zero (see also geo_weights or rescale_weights .
lambda: numeric between 0 and 1.
TM: target matrix (optional), default value is the covMcd from robustbase.
alpha: numeric, proportion of values included, between 0.5 and 1.
maxcond: optional, maximal condition number used for rho-estimation.
maxcsteps: maximal number of c-steps before algorithm stops.
n_initialhsets: number of initial h-sets, default is 6 times number of neighborhoods.

References

Puchhammer P. and Filzmoser P. (2023): Spatially smoothed robust covariance estimation for local outlier detection. tools:::Rd_expr_doi("10.48550/arXiv.2305.05371")

Examples

Run this code

# create data set
x1 = matrix(runif(200), ncol = 2)
x2 = matrix(rnorm(200), ncol = 2)
x = list(x1, x2)

# create weighting matrix
W = matrix(c(0, 1, 1, 0), ncol = 2)

# calculate ssMRCD
ssMRCD(x, weights = W, lambda = 0.5)