Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/Sboot_multireg.R
Calculates bootstrapped S-estimates of multivariate regression and corresponding bootstrap confidence intervals using the Fast and Robust Bootstrap method.
1 | Sboot_multireg(X, Y, R = 999, conf=0.95, ests = Sest_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. Default is |
conf |
level of the bootstrap confidence intervals. Default is |
ests |
S-estimates as returned by |
Called by FRBmultiregS
and typically not to
be used on its own. It requires the result of Sest_multireg
applied on X
and Y
,
supplied through the argument ests
. If ests
is not provided, Sest_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 and extended to multivariate regression by Van Aelst and Willems (2005).
The value centered
gives a matrix with R
columns and p*q+q*q rows (p is the number of explanatory variables
and q the number of response variables),
containing the recalculated S-estimates of the regression coefficients and the error covariance matrix.
Each column represents a different bootstrap sample.
The first p*q rows are the coefficient estimates, the next q*q rows represent the covariance estimate
(the estimates are vectorized, i.e. columns stacked on top of each other).
The 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 (BCa) 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 less than p distinct observations with positive weights are discarded
(a warning is given if this happens). The number of samples actually used is returned via ROK
.
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 |
cov |
bootstrap covariance matrix for the estimates in |
CI.bca |
a matrix containing bias corrected and accelerated confidence intervals corresponding to the
estimates in |
CI.basic |
a matrix containing basic bootstrap intervals corresponding to the
estimates in |
p.bca |
a vector containing p-values based on the bias corrected and accelerated confidence intervals (corresponding to the
estimates in |
p.basic |
a vector containing p-values based on the basic bootstrap intervals (corresponding to the
estimates in |
ROK |
number of bootstrap samples actually used (i.e. not discarded due to too few distinct observations with positive weight) |
Gert Willems, Ella Roelant and Stefan Van Aelst
A.C. Davison, D.V. Hinkley (1997) Bootstrap methods and their application. Cambridge University Press.
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 (2005) Multivariate regression S-estimators for robust estimation and inference. Statistica Sinica, 15, 981–1001.
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. URL: http://www.jstatsoft.org/v53/i03/.
FRBmultiregS
, Sest_multireg
, MMboot_multireg
1 2 3 4 5 6 7 | data(schooldata)
school.x <- data.matrix(schooldata[,1:5])
school.y <- data.matrix(schooldata[,6:8])
#computes 1000 bootstrap recalculations starting from the S-estimator
#obtained from Sest_multireg()
bootres <- Sboot_multireg(school.x,school.y,R=1000)
|
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