Rfit (version 0.14)

rfit: Rank-based Estimates of Regression Coefficients

Description

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

Usage

rfit(formula, data = list(), ...)## S3 method for class 'default':
rfit(formula, data=list(), yhat0 = NULL, scores = wscores, symmetric = FALSE, intercept = TRUE, ...)

Arguments

formula

an object of class formula

data

an optional data frame

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

intercept

use intercept = FALSE when 1 is in the column space of X or for regression through the orgin

...

additional arguments to be passed to fitting routines

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

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 L1 fit via rq.

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

data(baseball)
data(wscores)
fit<-rfit(weight~height,data=baseball)
summary(fit)