estLocScale {cellWise}

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)

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.

Value

A list with components:

• loc
  A vector with the estimated locations.

• scale
  A vector with the estimated scales.

Author(s)

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:
## Not run: 
vignette("wrap_examples")

## End(Not run)