FRB (version 2.0-1)

MMboot_loccov: Fast and Robust Bootstrap for MM-estimates of Location and Covariance

Description

Calculates bootstrapped MM-estimates of multivariate location and scatter using the Fast and Robust Bootstrap method.

Usage

MMboot_loccov(Y, R = 999, ests = MMest_loccov(Y))

Value

A list containing:

centered

recalculated MM- and S-estimates of location and scatter (centered by original estimates), see Details

MMest

original MM- and S-estimates of location and scatter, see Details

Arguments

Y

matrix or data frame.

R

number of bootstrap samples. Default is R=999.

ests

original MM-estimates as returned by MMest_loccov().

Author

Gert Willems, Ella Roelant and Stefan Van Aelst

Details

This function is called by FRBpcaMM and FRBhotellingMM, it is typically not to be used on its own. It requires the MM-estimates of multivariate location and scatter/shape (the result of MMest_loccov applied on Y), supplied through the argument ests. If ests is not provided, MMest_loccov calls the implementation of the multivariate MM-estimates in package rrcov of Todorov and Filzmoser (2009) with default arguments.

For multivariate data the fast and robust bootstrap was developed by Salibian-Barrera, Van Aelst and Willems (2006).

The value centered gives a matrix with R columns and \(2*(p+p*p)\) rows (\(p\) is the number of variables in Y), containing the recalculated estimates of the MM-location, MM-shape, S-covariance and S-location. Each column represents a different bootstrap sample. The first \(p\) rows are the MM-location estimates, the next \(p*p\) rows are the MM-shape estimates (vectorized). Then the next \(p*p\) rows are the S-covariance estimates (vectorized) and the final \(p\) rows are the S-location estimates. The estimates are centered by the original estimates, which are also returned through MMest in vectorized form.

References

• M. Salibian-Barrera, S. Van Aelst and G. Willems (2006) PCA based on multivariate MM-estimators with fast and robust bootstrap. Journal of the American Statistical Association, 101, 1198--1211.

• M. Salibian-Barrera, S. Van Aelst and G. Willems (2008) Fast and robust bootstrap. Statistical Methods and Applications, 17, 41--71.

• V. Todorov and P. Filzmoser (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. tools:::Rd_expr_doi("10.18637/jss.v032.i03").

• S. Van Aelst and G. Willems (2013), Fast and robust bootstrap for multivariate inference: The R package FRB. Journal of Statistical Software, 53(3), 1--32. tools:::Rd_expr_doi("10.18637/jss.v053.i03").

See Also

FRBpcaMM, FRBhotellingMM, Sboot_loccov

Examples

Y <- matrix(rnorm(50*5), ncol=5)
MMests <- MMest_loccov(Y) 
bootresult <- MMboot_loccov(Y, R = 1000, ests = MMests)