MMboot_multireg {FRB} | R Documentation |
Calculates bootstrapped MM-estimates of multivariate regression and corresponding bootstrap confidence intervals using the Fast and Robust Bootstrap method.
MMboot_multireg(X, Y, R, conf=0.95, ests = MMest_multireg(X, Y))
X |
a matrix or data frame containing the explanatory variables (possibly including intercept). |
Y |
a matrix or data frame containing the response variables. |
R |
number of bootstrap samples. |
conf |
level of the bootstrap confidence intervals. Default is conf=0.95 . |
ests |
MM-estimates as returned by MMest_multireg (). |
Called by FRBmultiregMM
and typically not to
be used on its own. It requires the result of MMest_multireg
applied on X
and Y
,
supplied through the argument ests
. If ests
is not provided, MMest_multireg
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.
The value centered
gives a matrix with R
columns and 2*(p*q+q*q) rows (p is the number of explanatory variables
and q the number of response variables),
containing the recalculated MM-estimates and initial S-estimates.
Each column represents a different bootstrap sample.
The first p*q rows are the MM-coefficient estimates, the next q*q rows represent the MM-estimate of the error shape matrix
(having determinant 1).
Then the next q*q rows are the S-estimate of error covariance and the final p*q rows are the S-estimates of the regression
coefficients (all estimates are vectorized, i.e. columns stacked on top of each other).
These 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).
A list containing the following components:
centered |
a matrix of all fast/robust bootstrap recalculations where the recalculations are centered by original estimates (see Details) |
vecest |
a vector containing the original estimates (see Details) |
SE |
bootstrap standard errors for the estimates in vecest |
CI.bca |
a matrix containing 95% 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 95% basic bootstrap intervals corresponding to the
estimates in vecest (first column are lower limits, second column are upper limits) |
Gert Willems and Ella Roelant
FRBmultiregMM
, MMest_multireg
, Sboot_multireg
data(schooldata) school.x <- data.matrix(schooldata[,1:5]) school.y <- data.matrix(schooldata[,6:8]) #computes 1000 bootstrap recalculations starting from the MM-estimator #obtained from MMest_multireg() bootres <- MMboot_multireg(school.x,school.y,R=1000)