FRB (version 2.0-1)

Sboot_loccov: Fast and Robust Bootstrap for S-estimates of location/covariance

Description

Calculates bootstrapped S-estimates using the Fast and Robust Bootstrap method.

Usage

Sboot_loccov(Y, R = 999, ests = Sest_loccov(Y))

Value

A list containing:

centered

recalculated estimates of location and covariance (centered by original estimates)

Sest

original estimates of location and covariance

Arguments

Y

matrix or data frame.

R

number of bootstrap samples. Default is R=999.

ests

original S-estimates as returned by Sest_loccov().

Author

Gert Willems, Ella Roelant and Stefan Van Aelst

Details

This function is called by FRBpcaS and FRBhotellingS, it is typically not to be used on its own. It requires the S-estimates of multivariate location and scatter/shape (the result of Sest_loccov applied on Y), supplied through the argument ests. If ests is not provided, Sest_loccov calls the implementation of the multivariate S-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 \(p+p*p\) rows (\(p\) is the number of variables in Y), containing the recalculated estimates of the S-location and -covariance. Each column represents a different bootstrap sample. The first \(p\) rows are the location estimates and the next \(p*p\) rows are the covariance estimates (vectorized). The estimates are centered by the original estimates, which are also returned through Sest.

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

FRBpcaS, FRBhotellingS, MMboot_loccov

Examples

Y <- matrix(rnorm(50*5), ncol=5)
Sests <- Sest_loccov(Y, bdp = 0.25) 
bootresult <- Sboot_loccov(Y, R = 1000, ests = Sests)