FRB (version 2.0-1)

MMboot_twosample: Fast and Robust Bootstrap for Two-Sample MM-estimates of Location and Covariance

Description

Calculates bootstrapped two sample MM-estimates using the Fast and Robust Bootstrap method.

Usage

MMboot_twosample(X, groups, R = 999, ests = MMest_twosample(X, groups))

Value

A list containing:

centered

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

MMest

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

Arguments

X

matrix of data frame.

groups

vector of 1's and 2's, indicating group numbers.

R

number of bootstrap samples. Default is R=999.

ests

original MM-estimates as returned by MMest_twosample().

Author

Ella Roelant, Gert Willems and Stefan Van Aelst

Details

This function is called by FRBhotellingMM, it is typically not to be used on its own. It requires the result of MMest_twosample applied on X, supplied through the argument ests. If ests is not provided, MMest_twosample will be called with default arguments.

The fast and robust bootstrap was first developed by Salibian-Barrera and Zamar (2002) for univariate regression MM-estimators and extended to the two sample setting by Roelant et al. (2008).

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

References

• E. Roelant, S. Van Aelst and G. Willems, (2008) Fast Bootstrap for Robust Hotelling Tests, COMPSTAT 2008: Proceedings in Computational Statistics (P. Brito, Ed.) Heidelberg: Physika-Verlag, 709--719.

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

• M. Salibian-Barrera, R.H. Zamar (2002) Bootstrapping robust estimates of regression. The Annals of Statistics, 30, 556--582.

• 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

See Also FRBhotellingMM, Sboot_twosample

Examples

# \donttest{
    Y1 <- matrix(rnorm(50*5), ncol=5)
    Y2 <- matrix(rnorm(50*5), ncol=5)
    Ybig <- rbind(Y1,Y2)
    grp <- c(rep(1,50),rep(2,50))
    MMests <- MMest_twosample(Ybig, grp)
    bootresult <- MMboot_twosample(Ybig, grp, R=500, ests=MMests)
# }