rfit {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(), ...)
## Default S3 method:
rfit(formula, data, subset, yhat0 = NULL, 
scores = Rfit::wscores, symmetric = FALSE, TAU = "F0", 
betahat0 = NULL, ...)

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 1 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

betahat0

a p by 1 vector of initial parameter estimates, default is NULL

...

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 residuals and the scored ranks of the residuals. That is, in rank-based 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; eg., linear (Wilcoxon) and normal (Gaussian) scores. If an inital fit is not supplied (i.e. yhat0 = NULL and betahat0 = NULL) then inital fit is based on a LS fit.

Esimation of scale parameter tau is provided which may be used for inference.

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, Joesph McKean

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 drop.test rstudent.rfit

Examples

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

### set the starting value
x1 <- runif(47); x2 <- runif(47); y <- 1 + 0.5*x1 + rnorm(47)
# based on a fit to a sub-model
rfit(y~x1+x2,yhat0=fitted.values(rfit(y~x1)))

### set value of delta used in estimation of tau ###
w <- factor(rep(1:3,each=3))
y <- rt(9,9)
rfit(y~w)$tauhat
rfit(y~w,delta=0.95)$tauhat  # recommended when n/p < 5