Various Tests of Robust Regression Estimates

DESCRIPTION:

Conducts test for bias of robust MM-estimates and Least Squares (LS) estimates against S-estimates, or permutation test of the slope estimate in a straight line fit.

USAGE:

test.lmRob(object, type="bias", level=NULL) 

REQUIRED ARGUMENTS:

object
an object of class "lmRob".

OPTIONAL ARGUMENTS:

type
character string. Valid choices are "bias" for bias test, or "permutation" for permutation test.
level
the level of the test for bias of MM-estimate. By default, the level component of object$robust.control is used.

VALUE:

the p-value of the permutation test, or an object of class "biasMM" representing the bias test, in which case the following components must be included:
mm
a list describing the test of bias for final MM-estimates, with the following components: stat, the t-statistic; pchi, the probability that a chi-squared random variable with degrees of freedom equal to object$rank is smaller than stat; qchi, the quantile of the chi-squared distribution with degrees of freedom equal to object$rank corresponding to the probability input in the level ( object$robust.control$level).
ls
a list describing the test of bias for LS-estimates, with the following components: stat, the t-statistic; pchi, the probability that a chi-squared random variable with degrees of freedom equal to object$rank is smaller than stat.
level
the level of the test for bias of MM-estimate.

REFERENCES:

Yohai, V., Stahel, W. A., and Zamar, R. H. (1991). A procedure for robust estimation and inference in linear regression, in Stahel, W. A. and Weisberg, S. W., Eds., Directions in robust statistics and diagnostics, Part II. Springer-Verlag.