ssMRCD {ssMRCD}

Spatially Smoothed MRCD Estimator

Description

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

Usage

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

Arguments

x

a list of matrices containing the observations per neighborhood sorted which can be obtained by the function restructure_as_list.

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.

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.

References

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

See Also

plot.ssMRCD, summary.ssMRCD, restructure_as_list

Examples

# 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)