sr.regression {SpatialNP}R Documentation

Multivariate regression based on spatial signs or ranks

Description

This function fits linear models to data using spatial signs or ranks.

Usage

 sr.regression(formula, data=NULL, score = c("sign", "rank"),
ae = TRUE, eps = 1e-06, na.action = na.fail) 

Arguments

formula a symbolic description of the model to be fit
data an optional matrix or a data frame
score a character string indicating which transformation of the observations should be used
ae logical. Should the result be affine equivariant?
eps tolerance for convergence
na.action a function which indicates what should happen when the data contain 'NA's. Default is to fail.

Details

See formula or lm for more details on specifying formulas.

The found matrix of coefficients β for a model

Y=X β^T+E

is the one that solves

X^T S(E(β))

where E(β) is the matrix of residuals corresponding to the choice of β and S(E(β) is the matrix of the chosen scores (signs or ranks) of those residuals.

The coefficient estimates found based on ranks (score = "rank") are always for the model with the intercept term included and the intercept is computed separately. To emphasize this when rank based coefficients are computed without the intercept term there is a row of NA values in the result.

Value

A matrix of estimated coefficients.

Author(s)

Jaakko Nevalainen, jaakko.nevalainen@uta.fi

See Also

tyler.shape, ae.hl.estimate

Examples

A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3)
X<-matrix(rt(150,1),ncol=3)
Y<-X%*%t(A)+runif(150,-1,1)
sr.regression(Y~X,data.frame(Y=Y,X=X),score="sign")
sr.regression(Y~X,data.frame(Y=Y,X=X),score="rank")

[Package SpatialNP version 0.9 Index]