| MMboot_loccov {FRB} | R Documentation |
Calculates bootstrapped MM-estimates of multivariate location and scatter using the Fast and Robust Bootstrap method.
MMboot_loccov(Y, R = 999, ests = MMest_loccov(Y))
Y |
matrix or data frame. |
R |
number of bootstrap samples. Default is |
ests |
original MM-estimates as returned by |
This function is called by FRBpcaMM and FRBhotellingMM, it is typically not to be used on its own.
It requires the MM-estimates of multivariate location and scatter/shape
(the result of MMest_loccov applied on Y), supplied through the argument ests.
If ests is not provided, MMest_loccov calls the implementation of the multivariate MM-estimates in package rrcov of Todorov and Filzmoser (2009) with default arguments.
For multivariate data the fast and robust bootstrap was developed by Salibian-Barrera, Van Aelst and Willems (2006).
The value centered gives a matrix with R columns and 2*(p+p*p) rows (p is the number of variables in Y),
containing the recalculated estimates of the MM-location, MM-shape, S-covariance and S-location.
Each column represents a different bootstrap sample.
The first p rows are the MM-location estimates, the next p*p rows are the MM-shape estimates (vectorized). Then the next
p*p rows are the S-covariance estimates (vectorized) and the final p rows are the S-location estimates.
The estimates are centered by the original estimates, which are also returned through MMest in vectorized form.
A list containing:
centered |
recalculated MM- and S-estimates of location and scatter (centered by original estimates), see Details |
MMest |
original MM- and S-estimates of location and scatter, see Details |
Gert Willems, Ella Roelant and Stefan Van Aelst
M. Salibian-Barrera, S. Van Aelst and G. Willems (2006) PCA based on multivariate MM-estimators with fast and robust bootstrap. Journal of the American Statistical Association, 101, 1198–1211.
M. Salibian-Barrera, S. Van Aelst and G. Willems (2008) Fast and robust bootstrap. Statistical Methods and Applications, 17, 41–71. regression.
V. Todorov and P. Filzmoser (2009) An Object-Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32, 1–47. URL http://www.jstatsoft.org/v32/i03/.
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/.
FRBpcaMM, FRBhotellingMM, Sboot_loccov
Y <- matrix(rnorm(50*5), ncol=5) MMests <- MMest_loccov(Y) bootresult <- MMboot_loccov(Y, R = 1000, ests = MMests)