hbrfit: High Breakdown Rank (HBR) Estimates

In kloke/hbrfit: High breakdown rank-based (HBR) estimation for linear models

High Breakdown Rank (HBR) Estimates

Description

High breakdown rank (HBR) estimates are robust to outliers in both X & Y spaces. They are based on a weighted Wilcoxon pseudo-norm. Data points which are outliers in both X & Y space are downweighted. HBR estimates achieve 50

Usage

hbrfit(formula, data, subset, symmetric = FALSE,...)

Arguments

formula	an object of class formula
data	an optional data frame
subset	an optional argument specifying the subset of observations to be used
symmetric	logical. If 'FALSE' uses median of residuals as estimate of intercept
...	additional arguments. Currently unused.

Details

The HBR pseudo-norm is ||u|| = sum_i < j b_ij |u_i - u_j|. The weights (b_ij) are chosen based on robust measures of distance. Data points with large residuals (based on a initial LTS fit) and outling design points (based on a robust measure of Mahalanobis distance) are down weighted (b_ij < 1). If all b_ij = 1 then the HBR pseudo-norm is the Wilcoxon. HBR estimates for linear models were developed by Chang, et. al. (1999). See also Section 3.12 of Hettmansperger and McKean (2011).

Value

coefficients	estimated regression coefficents with intercept
residuals	the residuals, i.e. y-yhat
fitted.values	yhat = x betahat
weights	estimated weights. the b_ij
x	original design matrix
y	original response vector
tauhat	estimated value of the scale parameter tau
taushat	estimated value of the scale parameter tau_s
betahat	estimated regression coefficents
qrx1	qrd of the design matrix with a column of ones prepended
call	Call to the function

Author(s)

Jeff Terpstra, Joe McKean, John Kloke

References

Chang, W. McKean, J.W., Naranjo, J.D., and Sheather, S.J. (1999), High breakdown rank-based regression, Journal of the American Statistical Association, 94, 205-219.

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Terpstra, J. and McKean, J.W. (2005), Rank-based analyses of linear models using R, Journal of Statistical Software, 14(7).

See Also

summary.hbrfit

Examples

data(stars)
hbrfit(light~temperature,data=stars)

kloke/hbrfit documentation built on Nov. 17, 2023, 2:33 p.m.