robreg3S {robreg3S}

Robust regression estimation and inference in the presence of cellwise and casewise contamination

Description

Finds 3S-robust regression estimator using the adaptive consistent filter.

Usage

	robreg3S(y, x, dummies=NULL, filter=TRUE, alpha=0.20, K=5, ...)

Arguments

y

vector of responses.

x

matrix of the numerical variables.

dummies

matrix of the dummy covariates, i.e., where each column are 0–1 vectors.

filter

logical, whether the filtering is used. Default value is TRUE.

alpha

1-alpha upper quantile (and alpha lower quantile) of the covariate distribution used in tail comparison in the first step. An exponential tail is used as the reference distribution. Default value is 0.20.

K

number of alternating M-S iterations in the estimation of the coefficients of the dummy covariates. Default value is 5. See Leung et al. for more details.

...

optional arguments to be used in the computation of GSE in the second step. See GSE

Details

This function computes 3S-robust regression as described in Leung et al. (2015).

If the model contains dummy variables (i.e., dummies != NULL), 3S-regression is computed using an iterative algorithm as described in Leung et al. (2015). Briefly, the algorithm first estimates the coefficients of the dummies using an M-estimator of regression and the coefficients of the continuous covariates using the original 3S-regression. See Leung et al. (2015) for more details.

Value

A list with components:

Summary.Table

Matrix of information available about the estimator. It contains regression coefficients, and for dummies != NULL, columns for the standard error, t-statistic, and p-value.

coef

vector of regression coefficients.

acov

matrix of the asymptotic covariate matrix, only for dummies != NULL.

resid

vector of residuals, that is the response minus the fitted values.

sigma.hat

the estimated residual standard error.

MD

the squared Mahalanobis distances of each observation based on the continuous covariates to the generalized location S-estimator with respect to the generalized scatter S-estimator.

xfilter

filtered matrix of the numerical variables from Step 1 of the estimator.

ximpute

matrix of the numerical variables with filtered cells imputed from Step 2 of the estimator.

weight

vector of the weights used in the estimation of the location generalized S-estimator. Not meant to be accessed.

Syx

estimated generalized S-scatter from Step 2. Not meant to be accessed.

myx

estimated generalized S-location from Step 2. Not meant to be accessed.

Author(s)

Andy Leung [e-mail], Hongyang Zhang, Ruben H. Zamar

References

Leung, A. , Zamar, R.H., and Zhang, H. Robust regression estimation and inference in the presence of cellwise and casewise contamination. arXiv:1509.02564.

See Also

GSE, generate.cellcontam.regress, generate.casecontam.regress, generate.casecontam.regress.dummies, generate.casecontam.regress.dummies

Examples

## Boston housing data
data(Boston, package="MASS")
boston <- Boston; rm(Boston)
boston$crim <- log(boston$crim)
boston$nox <- boston$nox^2
boston$rm <- boston$rm^2
boston$dis <- log(boston$dis)
boston$lstat <- log(boston$lstat)
boston$medv <- log(boston$medv)
boston$black <- boston$black/1000
boston$age <- boston$age/100
boston$tax <- boston$tax/100
boston$indus <- boston$indus/100
boston <- subset( boston, select=c(medv, crim, nox, rm, age, dis, tax, ptratio, black, lstat) )

## LS, MM, 3S
set.seed(100)
fit.LS <- lm(medv ~  ., data=boston)
fit.MM <- robustbase::lmrob(medv ~  ., data=boston)
fit.2S <- robreg3S( y=boston$medv, x=as.matrix(subset(boston,select=-medv)), filter = FALSE )
fit.3S <- robreg3S( y=boston$medv, x=as.matrix(subset(boston,select=-medv)) )

## Compare estimated coefficients
nrow(boston) *sum(( coef(fit.LS)[-1] - coef(fit.3S)[-1])^2* apply(boston[,-1], 2, mad)^2)
nrow(boston) *sum(( coef(fit.MM)[-1] - coef(fit.3S)[-1])^2* apply(boston[,-1], 2, mad)^2)
nrow(boston) *sum(( coef(fit.2S)[-1] - coef(fit.3S)[-1])^2* apply(boston[,-1], 2, mad)^2)

## Summary table
summary(fit.3S)