GSboot_multireg {FRB}R Documentation

Fast and Robust Bootstrap for GS-Estimates

Description

Calculates bootstrapped GS-estimates and bootstrap confidence intervals using the Fast and Robust Bootstrap method.

Usage

GSboot_multireg(X, Y, R, conf=0.95, ests = GSest_multireg(X, Y))

Arguments

X a matrix or data frame containing the explanatory variables.
Y a matrix or data frame containing the response variables.
R number of bootstrap samples
conf confidence level of the bootstrap confidence intervals. Default is conf=0.95
ests GS-estimates as returned by GSest_multireg()

Details

Called by FRBmultiregGS and typically not to be used on its own. If no original GS-estimates are provided the function uses the value of GSest_multireg.

The fast and robust bootstrap was first developed by Salibian-Barrera and Zamar (2002) for univariate regression MM-estimators.

The value centered gives a matrix with R columns and p*q+q*q rows (p is the number of explanatory variables without intercept and q is the number of response variables), containing the recalculated GS-estimates. Each column represents a different bootstrap sample. The first p*q rows are the recalculated slope estimates and the next q*q rows are the covariance estimates (the estimates are vectorized, i.e. columns stacked on top of each other). These bootstrap estimates are centered by the original estimates, which are also returned through vecest in vectorized form.

The output list further contains bootstrap standard errors, as well as so-called basic bootstrap confidence intervals and bias corrected and accelerated confidence intervals (Davison and Hinkley, 1997, p.194 and p.204 respectively). Also in the output are p-values defined as 1 minus the smallest confidence level for which the confidence intervals would include the (hypothesised) value of zero. Both BCa and basic bootstrap p-values are given. These are only useful for the regression coefficient estimates (not really for the covariance estimates).

Bootstrap samples which contain too few distinct observations with positive weights are discarded (a warning is given if this happens). The number of samples actually used is returned via ROK.

Value

A list containing the following components:

centered a matrix of all fast and robust bootstrap recalculations where the recalculations are centered by the original estimates (see Details).
vecest a vector containing the orginal estimates stacked on top of each other
SE bootstrap standard errors for the estimates in vecest
CI.bca a matrix containing bias corrected and accelerated confidence intervals, corresponding to the estimates in vecest (first column are lower limits, second column are upper limits)
CI.basic a matrix containing basic bootstrap intervals, corresponding to the estimates in vecest (first column are lower limits, second column are upper limits)
p.bca a vector containing p-values based on the bias corrected and accelerated confidence intervals (corresponding to the estimates in vecest)
p.basic a vector containing p-values based on the basic bootstrap intervals (corresponding to the estimates in vecest)
ROK number of bootstrap samples actually used (i.e. not discarded due to too few distinct observations with positive weight)

Author(s)

Ella Roelant and Gert Willems

References

See Also

GSest_multireg

Examples


data(schooldata)
school.x <- data.matrix(schooldata[,1:5])
school.y <- data.matrix(schooldata[,6:8])

#computes 10 bootstrap recalculations starting from the GS-estimator
#obtained from GSest_multireg
bootres <- GSboot_multireg(school.x,school.y,R=10)

[Package FRB version 1.6 Index]