Robust Statistical Methods

Robust (or "resistant") methods for statistics modelling have been available in S from the very beginning in the 1980s; and then in R in package `stats`

. Examples are `median()`

, `mean(*, trim = . )`

, `mad()`

, `IQR()`

, or also `fivenum()`

, the statistic behind `boxplot()`

in package `graphics`

) or `lowess()`

(and `loess()`

) for robust nonparametric regression, which had been complemented by `runmed()`

in 2003. Much further important functionality has been made available in recommended (and hence present in all R versions) package MASS (by Bill Venables and Brian Ripley, see *the* book Modern Applied Statistics with S). Most importantly, they provide `rlm()`

for robust regression and `cov.rob()`

for robust multivariate scatter and covariance.

This task view is about R add-on packages providing newer or faster, more efficient algorithms and notably for (robustification of) new models.

Please send suggestions for additions and extensions to the task view maintainer.

An international group of scientists working in the field of robust statistics has made efforts (since October 2005) to coordinate several of the scattered developments and make the important ones available through a set of R packages complementing each other. These should build on a basic package with "Essentials", coined robustbase with (potentially many) other packages building on top and extending the essential functionality to particular models or applications. Further, there is the quite comprehensive package robust, a version of the robust library of S-PLUS, as an R package now GPLicensed thanks to Insightful and Kjell Konis. Originally, there has been much overlap between 'robustbase' and 'robust', now robust *depends* on robustbase, the former providing convenient routines for the casual user where the latter will contain the underlying functionality, and provide the more advanced statistician with a large range of options for robust modeling.

We structure the packages roughly into the following topics, and typically will first mention functionality in packages robustbase and robust.

*Regression (Linear, Generalized Linear, Nonlinear Models, incl. Mixed Effects)*:`lmrob()`

(robustbase) and`lmRob()`

(robust) where the former uses the latest of the fast-S algorithms and heteroscedasticity and autocorrelation corrected (HAC) standard errors, the latter makes use of the M-S algorithm of Maronna and Yohai (2000), automatically when there are factors among the predictors (where S-estimators (and hence MM-estimators) based on resampling typically badly fail). The`ltsReg()`

and`lmrob.S()`

functions are available in robustbase, but rather for comparison purposes.`rlm()`

from MASS had been the first widely available implementation for robust linear models, and also one of the very first MM-estimation implementations. robustreg provides very simple M-estimates for linear regression (in pure R). Note that Koenker's quantile regression package quantreg contains L1 (aka LAD, least absolute deviations)-regression as a special case, doing so also for nonparametric regression via splines. Quantile regression (and hence L1 or LAD) for mixed effect models, is available in package lqmm, whereas an*MM-like*approach for robust linear**mixed effects**modeling is available from package robustlmm. Package mblm's function`mblm()`

fits median-based (Theil-Sen or Siegel's repeated) simple linear models. Package TEEReg provides trimmed elemental estimators for linear models. Generalized linear models (GLMs) are provided both via`glmrob()`

(robustbase) and`glmRob()`

(robust), where package robustloggamma focuses on generalized log gamma models. Robust ordinal regression is provided by rorutadis (UTADIS). Robust Nonlinear model fitting is available through robustbase's`nlrob()`

. multinomRob fits overdispersed multinomial regression models for count data. rgam and robustgam both fit robust GAMs, i.e., robust Generalized Additive Models. drgee fits "Doubly Robust" Generalized Estimating Equations (GEEs) complmrob does robust linear regression with compositional data as covariates.*Multivariate Analysis*: Here, the rrcov package which builds ("`Depends`

") on robustbase provides nice S4 class based methods, more methods for robust multivariate variance-covariance estimation, and adds robust PCA methodology. It is extended by rrcovNA, providing robust multivariate methods for*for incomplete*or missing (`NA`

) data, and by rrcovHD, providing robust multivariate methods for*High Dimensional*data. High dimensional data with an emphasis on functional data are treated robustly also by roahd. Specialized robust PCA packages are pcaPP (via Projection Pursuit), rpca (incl "sparse") and rospca. Historically, note that robust PCA can be performed by using standard R's`princomp()`

, e.g.,`X <- stackloss; pc.rob <- princomp(X, covmat= MASS::cov.rob(X))`

Here, robustbase contains a slightly more flexible version,`covMcd()`

than robust's`fastmcd()`

, and similarly for`covOGK()`

. OTOH, robust's`covRob()`

has automatically chosen methods, notably`pairwiseQC()`

for large dimensionality p. Package robustX for experimental, or other not yet established procedures, contains`BACON()`

and`covNCC()`

, the latter providing the neighbor variance estimation (NNVE) method of Wang and Raftery (2002), also available (slightly less optimized) in covRobust. RobRSVD provides a robust Regularized Singular Value Decomposition. mvoutlier (building on robustbase) provides several methods for outlier identification in high dimensions. GSE estimates multivariate location and scatter in the presence of missing data. RSKC provides**R**obust**S**parse**K**-means**C**lustering. robustDA for*robust mixture Discriminant Analysis*(RMDA) builds a mixture model classifier with noisy class labels. robcor computes robust pairwise correlations based on scale estimates, particularly on`FastQn()`

. covRobust provides the nearest neighbor variance estimation (NNVE) method of Wang and Raftery (2002).*Clustering (Multivariate)*: We are*not*considering cluster-resistant variance (/standard error) estimation (aka "sandwich"). Rather e.g. model based and hierarchical clustering methodology with a particular emphasis on robustness: Note that cluster's`pam()`

implementing "partioning around medians" is partly robust (medians instead of very unrobust k-means) but is*not*good enough, as e.g., the k clusters could consist of k-1 outliers one cluster for the bulk of the remaining data. "Truly" robust clustering is provided by packages genie, Gmedian, otrimle (trimmed MLE model-based) snipEM, (snipping EM) and qclust (robust estim. of Gaussian mixtures) and notably tclust (robust trimmed clustering). See also the CRAN task views Multivariate and Cluster*Large Data Sets*:`BACON()`

(in robustX) should be applicable for larger (n,p) than traditional robust covariance based outlier detectors. OutlierDM detects outliers for replicated high-throughput data. (See also the CRAN task view MachineLearning.)*Descriptive Statistics / Exploratory Data Analysis*:`boxplot.stats()`

, etc mentioned above*Time Series*:- R's
`runmed()`

provides*most robust*running median filtering. - Package robfilter contains robust regression and filtering methods for univariate time series, typically based on repeated (weighted) median regressions.
- The RobPer provides several methods for robust periodogram estimation, notably for irregularly spaced time series.
- Peter Ruckdeschel has started to lead an effort for a robust time-series package, see robust-ts on R-Forge.
- Further, robKalman,
*"Routines for Robust Kalman Filtering --- the ACM- and rLS-filter"*, is being developed, see robkalman on R-Forge.

- R's
*Econometric Models*: Econometricians tend to like HAC (heteroscedasticity and autocorrelation corrected) standard errors. For a broad class of models, these are provided by package sandwich. Note that`vcov(lmrob())`

also uses a version of HAC standard errors for its robustly estimated linear models. See also the CRAN task view Econometrics*Robust Methods for Bioinformatics*: There are several packages in the Bioconductor project providing specialized robust methods. In addition, RobLoxBioC provides infinitesimally robust estimators for preprocessing omics data.*Robust Methods for Survival Analysis*: Package coxrobust provides robust estimation in the Cox model. OutlierDC detects outliers using quantile regression for censored data.*Robust Methods for Surveys*: On R-forge only, package rhte provides a robust Horvitz-Thompson estimator.*Geostatistics*: Package georob aims at robust geostatistical analysis of spatial data, such as kriging and more.*Collections of several methodologies*:- WRS2 contains robust tests for ANOVA and ANCOVA and other functionality from Rand Wilcox's collection.
- walrus builds on WRS2's computations, providing a different user interface.
- robeth contains R functions interfacing to the extensive RobETH fortran library with many functions for regression, multivariate estimation and more.

*Other approaches to robust and resistant methodology*:- The package distr and its several child packages also allow to explore robust estimation concepts, see e.g., distr on R-Forge.
- Notably, based on these, the project robast aims for the implementation of R packages for the computation of optimally robust estimators and tests as well as the necessary infrastructure (mainly S4 classes and methods) and diagnostics; cf. M. Kohl (2005). It includes the R packages RandVar, RobAStBase, RobLox, RobLoxBioC, RobRex. Further, ROptEst, and ROptRegTS.
- RobustAFT computes Robust Accelerated Failure Time Regression for Gaussian and logWeibull errors.
- robumeta for robust variance meta-regression; metaplus adds robustness via t- or mixtures of normal distributions.
- ssmrob provides robust estimation and inference in sample selection models.

a year ago

Martin Maechler

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