rrcovNA (version 0.5-2)

CovNASest: S Estimates of Multivariate Location and Scatter for incomplete data

Description

Computes S-Estimates of multivariate location and scatter based on Tukey's biweight function for incomplete data using a fast algorithm similar to the one proposed by Salibian-Barrera and Yohai (2006) for the case of regression. Alternativley, the Ruppert's SURREAL algorithm, bisquare or Rocke type estimation can be used.

Usage

CovNASest(x, bdp = 0.5, arp = 0.1, eps = 1e-5, maxiter = 120,
        nsamp = 500, impMeth = c("norm" , "seq", "rseq"), seed = NULL, 
        trace = FALSE, tolSolve = 1e-13,
        scalefn,
        method = c("sfast", "surreal", "bisquare", "rocke", "suser", "sdet"), control,
        t0, S0, initcontrol)

Value

An S4 object of class CovNASest which is a subclass of the virtual class CovNARobust.

Arguments

x

a matrix or data frame.

bdp

a numeric value specifying the required breakdown point. Allowed values are between (n - p)/(2 * n) and 1 and the default is bdp=0.5.

arp

a numeric value specifying the asympthotic rejection point (for the Rocke type S estimates), i.e. the fraction of points receiving zero weight (see Rocke (1996)). Default is arp=0.1.

eps

a numeric value specifying the relative precision of the solution of the S-estimate (bisquare and Rocke type). Default is to eps=1e-5.

maxiter

maximum number of iterations allowed in the computation of the S-estimate (bisquare and Rocke type). Default is maxiter=120.

nsamp

the number of random subsets considered. Default is nsamp = 500.

impMeth

select imputation method to use - choose one of "norm" , "seq" or "rseq". The default is "norm"

seed

starting value for random generator. Default is seed = NULL.

trace

whether to print intermediate results. Default is trace = FALSE.

tolSolve

numeric tolerance to be used for inversion (solve) of the covariance matrix in mahalanobis.

scalefn

function to compute a robust scale estimate or character string specifying a rule determining such a function. Used for computing the "deterministic" S-estimates (method="sdet"). If scalefn is missing or is NULL, the function is selected depending on the data set size, following the recomendation of Hubert et al. (2012) - Qn if n <= 1000 and scaleTau2 otherwise.

method

Which algorithm to use: 'sfast'=FAST-S, 'surreal'=SURREAL, 'bisquare', 'rocke' or 'sdet', which will invoke the deterministic algorihm of Hubert et al. (2012).

control

a control object (S4) of class CovControlSest-class containing estimation options - same as these provided in the fucntion specification. If the control object is supplied, the parameters from it will be used. If parameters are passed also in the invocation statement, they will override the corresponding elements of the control object.

t0

optional initial HBDP estimate for the center

S0

optional initial HBDP estimate for the covariance matrix

initcontrol

optional control object to be used for computing the initial HBDP estimates

Author

Valentin Todorov , Matias Salibian-Barrera and Victor Yohai . See also the code from Kristel Joossens, K.U. Leuven, Belgium and Ella Roelant, Ghent University, Belgium.

Details

Computes biweight multivariate S-estimator of location and scatter. The computation will be performed by one of the following algorithms:

FAST-S

An algorithm similar to the one proposed by Salibian-Barrera and Yohai (2006) for the case of regression

SURREAL

Ruppert's SURREAL algorithm when method is set to 'surreal'

BISQUARE

Bisquare S-Estimate with method set to 'bisquare'

ROCKE

Rocke type S-Estimate with method set to 'rocke'

.

References

M. Salibian-Barrera and V. Yohai (2006) A fast algorithm for S-regression estimates, Journal of Computational and Graphical Statistics, 15, 414--427.

R. A. Maronna, D. Martin and V. Yohai (2006). Robust Statistics: Theory and Methods. Wiley, New York.

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. <doi:10.18637/jss.v032.i03>.

Examples

library(rrcov)
data(bush10)
CovNASest(bush10)

## the following four statements are equivalent
c0 <- CovNASest(bush10)
c1 <- CovNASest(bush10, bdp = 0.25)
c2 <- CovNASest(bush10, control = CovControlSest(bdp = 0.25))
c3 <- CovNASest(bush10, control = new("CovControlSest", bdp = 0.25))

## direct specification overrides control one:
c4 <- CovNASest(bush10, bdp = 0.40,
             control = CovControlSest(bdp = 0.25))
c1
summary(c1)

## Use the SURREAL algorithm of Ruppert
cr <- CovNASest(bush10, method="surreal")
cr

## Use Bisquare estimation
cr <- CovNASest(bush10, method="bisquare")
cr

## Use Rocke type estimation
cr <- CovNASest(bush10, method="rocke")
cr