FRB (version 2.0-1)

Sboot_twosample: Fast and Robust Bootstrap for Two-Sample S-estimates of Location and Covariance

Description

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

Usage

Sboot_twosample(X, groups, R = 999, ests = Sest_twosample(X, groups))

Value

A list containing:

centered

recalculated estimates of location of first and second center and covariance (centered by original estimates)

Sest

original estimates of first and second center and common covariance

Arguments

X

matrix or data frame.

groups

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

R

number of bootstrap samples. Default is R=999.

ests

original two-sample S-estimates as returned by Sest_twosample().

Author

Ella Roelant, Gert Willems and Stefan Van Aelst

Details

This function is called by FRBhotellingS, it is typically not to be used on its own. It requires the result of Sest_twosample applied on X, supplied through the argument ests. If ests is not provided, Sest_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 \(2*p+p*p\) rows (\(p\) is the number of variables in X), containing the recalculated estimates of the S-location for the first and second center and common S-covariance. Each column represents a different bootstrap sample. The first \(p\) rows are the location estimates of the first center, the next \(p\) rows are the location estimates of the second center and the last \(p*p\) rows are the common covariance estimates (vectorized). The estimates are centered by the original estimates, which are also returned through Sest.

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

FRBhotellingS

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))
    Sests <- Sest_twosample(Ybig, grp, bdp=0.25)
    bootresult <- Sboot_twosample(Ybig,grp,R=1000,ests=Sests)
# }