rfit: Rank-based Estimates of Regression Coefficients

In kloke/Rfit: Rank-Based Estimation for Linear Models

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", ...)

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. linear (Wilcoxon) and normal (Gaussian) scores. If an inital fit is not supplied (i.e. yhat0 = NULL) then inital fit is based on a LS fit.

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)))

kloke/Rfit documentation built on Sept. 9, 2023, 7:20 p.m.