rfit function

Rank-based Estimates of Regression Coefficients

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

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.

Returns

• 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

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.

Author(s)

John Kloke, Joesph McKean

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