hbrfit | R Documentation |
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
hbrfit(formula, data, subset, symmetric = FALSE,...)
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. |
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).
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 |
Jeff Terpstra, Joe McKean, John Kloke
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).
summary.hbrfit
data(stars)
hbrfit(light~temperature,data=stars)
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