existsPIC-methods: Methods for Function existsPIC in Package `distrMod'
Description
existsPIC-methods to check whether in a given L2 differentiable model at parameter value theta there exist
(partial) influence curves to Trafo $D_\theta$.Usage
existsPIC(object, ...)
## S3 method for class 'L2ParamFamily':
existsPIC(object, warning = TRUE, tol = .Machine$double.eps)
Arguments
...
further arguments used by specific methods.
warning
logical: should a warning be issued if there exist no (partial) influence curves?
tol
the tolerance the linear algebraic operations. Default is .Machine$double.eps.
concept
- partial influence curve
- bounded influence curve
- existence of influence curves
- influence curve
Details
To check the existence of (partial) influence curves and, simultaneously, for bounded
(partial) influence curves, by Lemma 1.1.3 in Kohl(2005) [resp. the fact that ${\rm ker} I={\rm ker} J$
for $J= {\rm E} (\Lambda',1)' (\Lambda',1) w$ and
$w={\rm min}(1, b/|(\Lambda',1)|$], it suffices to check that
${\rm ker }I$ is a subset of ${\rm ker }D_\theta$. This is done by
a call to isKerAinKerB.References
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness.
Bayreuth: Dissertation.