cellMCD {cellWise}

cellWise minimum covariance determinant estimator

Description

The cellwise minimum covariance determinant estimator computes cellwise robust estimates of the center and covariance matrix of a data set X. The algorithm guarantees a monotone decrease of an objective function, which is based on observed Gaussian log-likelihood. By default, it starts by calling checkDataSet to clean the data.

Usage

cellMCD(X, alpha = 0.75, quant = 0.99,
        crit = 1e-4, noCits = 100, lmin = 1e-4,
        checkPars = list())

Arguments

X

X is the input data, and must be an n by d matrix or a data frame.

alpha

In each column, at least n*alpha cells must remain unflagged. Defaults to 75%, should not be set (much) lower.

quant

Determines the cutoff value to flag cells. Defaults to 0.99.

crit

The iteration stops when successive covariance matrices (of the standardized data) differ by less than crit. Defaults to 1e-4.

noCits

The maximal number of C-steps used.

lmin

a lower bound on the eigenvalues of the estimated covariance matrix on the standardized data. Defaults to 1e-4. Should not be smaller than 1e-6.

checkPars

Optional list of parameters used in the call to checkDataSet. The options are:

• coreOnly
  If TRUE, skip the execution of checkDataset. Defaults to FALSE.

• numDiscrete
  A column that takes on numDiscrete or fewer values will be considered discrete and not retained in the cleaned data. Defaults to 5.

• fracNA
  Only retain columns and rows with fewer NAs than this fraction. Defaults to 0.5.

• precScale
  Only consider columns whose scale is larger than precScale. Here scale is measured by the median absolute deviation. Defaults to 1e-12.

• silent
  Whether or not the function progress messages should be suppressed. Defaults to FALSE.

Details

The matrix raw.S in the output is the raw estimate of scatter produced by cellMCD. The final S is obtained from raw.S by rescaling such that its diagonal entries equal the squares of the univariate scales in locsca$scale. This reduces the bias at Gaussian data, which matters mainly for large sample sizes.

Value

A list with components:

• mu
  the cellMCD estimate of location.

• S
  the cellMCD estimate of scatter, after bias correction (see details).

• W
  the cellMCD estimate of W, a binary matrix indicating all outlying cells as zero.

• preds
  predictions (=conditional expectations) of the flagged cells, given the clean cells in the same row.

• csds
  conditional standard deviations of the flagged cells, given the clean cells in the same row.

• Ximp
  imputed data matrix.

• Zres
  matrix of cellwise standardized residuals.

• raw.S
  the raw cellMCD estimate of scatter, without bias correction.

• locsca
  list containing robust locations and scales used to standardize the data before running the algorithm. The results m, S, preds, Ximp are returned in their original location/scale.

• nosteps
  number of steps the algorithm took to converge.

• X
  the data on which the algorithm was executed.

• quant
  the cutoff used to flag the cells.

Author(s)

J. Raymaekers and P.J. Rousseeuw

References

J. Raymaekers and P.J. Rousseeuw (2022). The cellwise MCD estimator, Journal of the American Statistical Association, to appear. doi:10.1080/01621459.2023.2267777(link to open access pdf)

See Also

plot_cellMCD

Examples

mu    <- rep(0, 3)
Sigma <- diag(3) * 0.5 + 0.5
set.seed(123)
X <- MASS::mvrnorm(1000, mu, Sigma)
X[1:5, 1]  <- X[1:5, 1] + 5
X[6:10, 2] <- X[6:10, 2] - 10
X[12, 1:2] <- c(-4,8)
colnames(X) <- c("X1","X2","X3")
cellMCD.out <- cellMCD(X)
cellMCD.out$mu
cov2cor(cellMCD.out$S)
cellMCD.out$W[1:15,]
cellMCD.out$Ximp[1:15,]
cellMap(cellMCD.out$Zres[1:15,])

# For more examples, we refer to the vignette:
## Not run: 
vignette("cellMCD_examples")

## End(Not run)