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

In FRB: Fast and Robust Bootstrap

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))

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().

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.

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

Author(s)

Ella Roelant, Gert Willems and Stefan Van Aelst

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v053.i03")}.

See Also

See Also FRBhotellingMM, Sboot_twosample

Examples

    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)

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