robustX: mvBACON – R documentation

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mvBACON

BACON: Blocked Adaptive Computationally-Efficient Outlier Nominators

Description

This function performs an outlier identification algorithm to the data in the x array [n x p] and y vector [n] following the lines described by Hadi et al. for their BACON outlier procedure.

Usage

mvBACON(x, collect = 4, m = min(collect * p, n * 0.5), alpha = 0.95,
        init.sel = c("Mahalanobis", "dUniMedian", "random", "manual"),
        man.sel, maxsteps = 100, allowSingular = FALSE, verbose = TRUE)

Arguments

`x`	numeric matrix (of dimension [n x p]), not supposed to contain missing values.
`collect`	a multiplication factor c, when `init.sel` is not `"manual"`, to define m, the size of the initial basic subset, as c p, in practice, `m <- min(p collect, n/2)`.
`m`	integer in `1:n` specifying the size of the initial basic subset; used only when `init.sel` is not `"manual"`.
`alpha`	significance level for the chisq cutoff, used to define the next iterations basic subset.
`init.sel`	character string, specifying the initial selection mode; implemented modes are: "Mahalanobis" based on Mahalanobis distances (default); the version V1 of the reference; affine invariant but not robust. "dUniMedian" based on the distances from the univariate medians; ; the version V2 of the reference; robust but not affine invariant. "random" based on a random selection, i.e., reproducible only via `set.seed()`. "manual" based on manual selection; in this case, a vector `man.sel` containing the indices of the selected observations must be specified. `"Mahalanobis"`, `"dUniMedian"` where proposed by Hadi and the other authors in the reference as versions ‘V_1’ and ‘V_2’, as well as `"manual"`, while `"random"` is provided in order to study the behaviour of BACON.
`man.sel`	only when `init.sel == "manual"`, the indices of observations determining the initial basic subset (and `m <- length(man.sel)`).
`maxsteps`	maximal number of iteration steps.
`allowSingular`	logical indicating a solution should be sought also when no matrix of rank p is found.
`verbose`	logical indicating if messages are printed which trace progress of the algorithm.

Value

a list with components

`subset`	logical vector of length `n` where the `i`-th entry is true iff the i-th observation is part of the final selection.
`dis`	numeric vector of length `n` with the (Mahalanobis) distances.
`cov`	p x p matrix, the corresponding robust estimate of covariance.

Author(s)

Ueli Oetliker, Swiss Federal Statistical Office, for S-plus 5.1. Port to R, testing etc, by Martin Maechler

References

Billor, N., Hadi, A. S., and Velleman , P. F. (2000). BACON: Blocked Adaptive Computationally-Efficient Outlier Nominators; Computational Statistics and Data Analysis 34, 279–298. doi: 10.1016/S0167-9473(99)00101-2

Examples

require(robustbase) # for example data and covMcd():
## simple 2D example :
 plot(starsCYG, main = "starsCYG  data  (n=47)")
 B.st <- mvBACON(starsCYG)
 points(starsCYG[ ! B.st$subset,], pch = 4, col = 2, cex = 1.5)
 stopifnot(identical(which(!B.st$subset), c(7L,9L,11L,14L,20L,30L,34L)))
 ## finds the clear outliers (and 3 "borderline")

 ## 'coleman' from pkg 'robustbase'
 coleman.x <- data.matrix(coleman[, 1:6])
 Cc <- covMcd (coleman.x) # truly robust
 summary(Cc) # -> 6 outliers (1,3,10,12,17,18)
 Cb1 <- mvBACON(coleman.x) ##-> subset is all TRUE hmm??
 Cb2 <- mvBACON(coleman.x, init.sel = "dUniMedian")
 stopifnot(all.equal(Cb1, Cb2))
 Cb.r <- lapply(1:20, function(i) { set.seed(i)
                     mvBACON(coleman.x, init.sel="random", verbose=FALSE) })
 nm <- names(Cb.r[[1]]); nm <- nm[nm != "steps"]
 all(eqC <- sapply(Cb.r[-1], function(CC) all.equal(CC[nm], Cb.r[[1]][nm]))) # TRUE
 ## --> BACON always  breaks down, i.e., does not see the outliers here
 ## breaks down even when manually starting with all the non-outliers:
 Cb.man <- mvBACON(coleman.x, init.sel = "manual",
                   man.sel = setdiff(1:20, c(1,3,10,12,17,18)))
 which( ! Cb.man$subset) # the outliers according to mvBACON : _none_

robustX

'eXtra' / 'eXperimental' Functionality for Robust Statistics

v1.2-4

GPL (>= 2)

Authors

Werner Stahel, Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>) and potentially others

Initial release

2019-02-25