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

In FRB: Fast and Robust Bootstrap

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))

Arguments

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

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.

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

Author(s)

Gert Willems, Ella Roelant and Stefan Van Aelst

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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)

FRB documentation built on Oct. 7, 2024, 5:09 p.m.