Rank-based Estimates of Regression Coefficients

Description

Minimizes Jaeckel's dispersion function to obtain a rank-based solution for linear models.

Usage

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rfit(formula, data = list(), ...)

## Default S3 method:
rfit(formula, data, subset, yhat0 = NULL, 
scores = Rfit::wscores, symmetric = FALSE, TAU = "F0", ...)

Arguments

formula

an object of class formula

data

an optional data frame

subset

an optional argument specifying the subset of observations to be used

yhat0

an n by vector of initial fitted values, default is NULL

scores

an object of class 'scores'

symmetric

logical. If 'FALSE' uses median of residuals as estimate of intercept

TAU

version of estimation routine for scale parameter. F0 for Fortran, R for (slower) R, N for none

...

additional arguments to be passed to fitting routines

Details

Rank-based estimation involves replacing the L2 norm of least squares estimation with a pseudo-norm which is a function of the ranks of the residuals. That is, in rank estimation, the usual notion of Euclidean distance is replaced with another measure of distance which is referred to as Jaeckel's (1972) dispersion function. Jaeckel's dispersion function depends on a score function and a library of commonly used score functions is included. e.g. Wilcoxon and sign score functions. If an inital fit is not supplied (i.e. yhat0 = NULL) then inital fit is based on an LS fit via lm.

Value

coefficients

estimated regression coefficents with intercept

residuals

the residuals, i.e. y-yhat

fitted.values

yhat = x betahat

xc

centered design matrix

tauhat

estimated value of the scale parameter tau

taushat

estimated value of the scale parameter tau_s

betahat

estimated regression coefficents

call

Call to the function

Author(s)

John Kloke kloke@biostat.wisc.edu

References

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

Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of residuals. Annals of Mathematical Statistics, 43, 1449 - 1458.

Jureckova, J. (1971). Nonparametric estimate of regression coefficients. Annals of Mathematical Statistics, 42, 1328 - 1338.

See Also

summary.rfit

Examples

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