cellWise (version 2.5.3)

estLocScale: Estimate robust location and scale

Description

Estimate a robust location estimate and scale estimate of every column in X.

Usage

estLocScale(X, type = "wrap", precScale = 1e-12,
center = TRUE, alpha = 0.5, nLocScale = 25000, silent = FALSE)

Value

A list with components:

• loc
  A vector with the estimated locations.

• scale
  A vector with the estimated scales.

Arguments

X

The input data. It must be an \(n\) by \(d\) matrix or a data frame.

type

The type of estimators used. One of:

• "1stepM":
  The location is the 1-step M-estimator with the biweight psi function. The scale estimator is the 1-step M-estimator using a Huber rho function with \(b = 2.5\).

• "mcd":
  the location is the weighted univariate MCD estimator with cutoff
  \(\sqrt(qchisq(0.975,1))\). The scale is the corresponding weighted univariate MCD estimator, with a correction factor to make it approximately unbiased at gaussian data.

• "wrap":
  Starting from the initial estimates corresponding to option "mcd", the location is the 1-step M-estimator with the wrapping psi function with \(b = 1.5\) and \(c = 4\). The scale estimator is the same as in option "mcd".

Defaults to "wrap".

precScale

The precision scale used throughout the algorithm. Defaults to \(1e-12\).

center

Whether or not the data has to be centered before calculating the scale. Not in use for type = "mcd". Defaults to TRUE.

alpha

The value of \(\alpha\) in the univariate mcd, must be between 0.5 and 1. The subsetsize is \(h = \lceil \alpha n \rceil\). Only used for type = "mcd". Defaults to \(\alpha = 0.5\).

nLocScale

If nLocScale \(< n\), nLocScale observations are sampled to compute the location and scale. This speeds up the computation if \(n\) is very large. When nLocScale \(= 0\) all observations are used. Defaults to nLocScale \(= 25000\).

silent

Whether or not a warning message should be printed when very small scales are found. Defauts to FALSE.

Author

Raymaekers, J. and Rousseeuw P.J.

References

Raymaekers, J., Rousseeuw P.J. (2019). Fast robust correlation for high dimensional data. Technometrics, 63(2), 184-198. (link to open access pdf)

See Also

wrap

Examples

library(MASS) 
set.seed(12345) 
n = 100; d = 10
X = mvrnorm(n, rep(0, 10), diag(10))
locScale = estLocScale(X)
# For more examples, we refer to the vignette:
if (FALSE) {
vignette("wrap_examples")
}