rrcovNA (version 0.4-8)

CovNAMcd: Robust Location and Scatter Estimation via MCD for incomplete data

Description

Computes a robust multivariate location and scatter estimate with a high breakdown point for incomplete data, using the ‘Fast MCD’ (Minimum Covariance Determinant) estimator.

Usage

CovNAMcd(x, alpha = 1/2, nsamp = 500, seed = NULL, trace = FALSE, 
use.correction = TRUE, impMeth = c("norm" , "seq", "rseq"), control)

Arguments

x

a matrix or data frame.

alpha

numeric parameter controlling the size of the subsets over which the determinant is minimized, i.e., alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5.

nsamp

number of subsets used for initial estimates or "best" or "exact". Default is nsamp = 500. For nsamp="best" exhaustive enumeration is done, as long as the number of trials does not exceed 5000. For "exact", exhaustive enumeration will be attempted however many samples are needed. In this case a warning message will be displayed saying that the computation can take a very long time.

seed

starting value for random generator. Default is seed = NULL

trace

whether to print intermediate results. Default is trace = FALSE

use.correction

whether to use finite sample correction factors. Default is use.correction=TRUE

impMeth

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

control

a control object (S4) of class CovControlMcd-class containing estimation options - same as these provided in the function 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.

Value

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

Details

This function computes the minimum covariance determinant estimator of location and scatter and returns an S4 object of class CovMcd-class containing the estimates. The implementation of the function is similar to the existing R function covMcd() which returns an S3 object. The MCD method looks for the $h (> n/2)$ observations (out of $n$) whose classical covariance matrix has the lowest possible determinant. The raw MCD estimate of location is then the average of these $h$ points, whereas the raw MCD estimate of scatter is their covariance matrix, multiplied by a consistency factor and a finite sample correction factor (to make it consistent at the normal model and unbiased at small samples). Both rescaling factors are returned also in the vector raw.cnp2 of length 2. Based on these raw MCD estimates, a reweighting step is performed which increases the finite-sample efficiency considerably - see Pison et al. (2002). The rescaling factors for the reweighted estimates are returned in the vector cnp2 of length 2. Details for the computation of the finite sample correction factors can be found in Pison et al. (2002). The finite sample corrections can be suppressed by setting use.correction=FALSE. The implementation in rrcov uses the Fast MCD algorithm of Rousseeuw and Van Driessen (1999) to approximate the minimum covariance determinant estimator.

References

V. Todorov, M. Templ and P. Filzmoser. Detection of multivariate outliers in business survey data with incomplete information. Advances in Data Analysis and Classification, 5 37--56, 2011. P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223.

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. URL http://www.jstatsoft.org/v32/i03/.

Examples

    data(bush10)
    mcd <- CovNAMcd(bush10)
    mcd
    summary(mcd)

    plot(mcd)
    plot(mcd, which="pairs")
    plot(mcd, which="xydistance")
    plot(mcd, which="xyqqchi2")