snipEM: Snipping for location and scatter estimation with cellwise...
In snipEM: Snipping Methods for Robust Estimation and Clustering

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes an estimator optimizing the Gaussian likelihood over a snipping set. The function snipEM.initialV can be used to perform some iterations to initialize V.

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snipEM(X, V, tol = 1e-04, maxiters = 500, maxiters.S = 1000, print.it = FALSE) 

snipEM.initialV(X, V, mu0, S0, maxiters.S = 100, greedy = TRUE)

`X`	Data.
`V`	Binary matrix of the same size as `X`. Zeros correspond to initial snipped entries.
`tol`	Tolerance for convergence. Default is `1e-4`.
`maxiters`	Maximum number of iterations for the SM algorithm. Default is `500`.
`maxiters.S`	Maximum number of iterations of the inner greedy snipping algorithm. Default is `1000`.
`print.it`	Logical; if `TRUE`, partial results are print. Default is `FALSE`.
`mu0`	Initial estimate for the mean vector that is used in the initialization stage.
`S0`	Initial estimate for the covariance matrix that is used in the initialization stage.
`greedy`	Logical; if `TRUE`, perform the greedy snipping algorithm in search for the binary matrix that gives the largest likelihood value throughout `maxiters.S` iterations. If `FALSE`, stop right after the snipping algorithm finds a binary matrix that gives a larger likelihood value than the initial one. Default is `TRUE`.

This function computes the sclust estimator of Farcomeni (2014) with k=1. It therefore provides a robust estimate of location and scatter in presence of entry-wise outliers. It is based on a snip-maximize (SM) algorithm. At the S step, the likelihood is optimized over the set of snipped entries, at the M step the location and scatter estimates are updated. The S step is based on a greedy algorithm, unlike the one proposed in Farcomeni (2014,2014a). The number of snipped entries sum(1-V) is kept fixed throughout.

Results depend on good initialization of the V matrix. A boxplot rule (see examples) usually works well. The function snipEM.initialV can be used to improve the initial choice through some iterations updating only V from initial (robust) estimates mu0 and S0. In the example, the EMVE is used to obtain mu0 and S0.

A list with the following elements:

`mu`	Estimated location.
`S`	Estimated scatter matrix.
`V`	Final (optimal) V matrix.
`lik`	Gaussian log-likelihood at convergence.
`iter`	Number of outer iterations before convergence.

Alessio Farcomeni alessio.farcomeni@uniroma1.it, Andy Leung andy.leung@stat.ubc.ca

Farcomeni, A. (2014) Snipping for robust k-means clustering under component-wise contamination, Statistics and Computing, 24, 909-917

Farcomeni, A. (2014) Robust constrained clustering in presence of entry-wise outliers, Technometrics, 56, 102-111

sclust, stEM, sumlog, ldmvnorm

n=100
p=5
Xc <- matrix(rnorm(100*10),100,5)

# initial V 
V <- matrix(1,n,p)
V[!is.na(match(as.vector(Xc),boxplot(as.vector(Xc),plot=FALSE)$out))] <- 0
Xna <- Xc 
Xna[ which( V == 0) ] <- NA

resSEM <- snipEM(Xc, V)