Sboot_loccov function

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

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

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

Arguments

• Y: matrix or data frame.
• R: number of bootstrap samples. Default is R=999.
• ests: original S-estimates as returned by Sest_loccov().

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.

Returns

A list containing: - centered: recalculated estimates of location and covariance (centered by original estimates)

• Sest: original estimates of location and covariance

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") .

Author(s)

Gert Willems, Ella Roelant and Stefan Van Aelst

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)