Generates an object of class "L2ParamFamily".
L2ParamFamily(name, distribution = Norm(), distrSymm,
main = main(param), nuisance = nuisance(param),
fixed = fixed(param), trafo = trafo(param),
param = ParamFamParameter(name = paste("Parameter of", name),
main = main, nuisance = nuisance,
fixed = fixed, trafo = trafo),
props = character(0),
startPar = NULL, makeOKPar = NULL,
modifyParam = function(theta){ Norm(mean=theta) },
L2deriv.fct = function(param) {force(theta <- param@main)
return(function(x) {x-theta})},
L2derivSymm, L2derivDistr, L2derivDistrSymm,
FisherInfo.fct, FisherInfo = FisherInfo.fct(param),
.returnClsName = NULL, .withMDE = TRUE)character string: name of the family
object of class "Distribution":
member of the family
object of class "DistributionSymmetry":
symmetry of distribution.
numeric vector: main parameter
numeric vector: nuisance parameter
numeric vector: fixed part of the parameter
function in param or matrix: transformation of the parameter
object of class "ParamFamParameter":
parameter of the family
startPar is a function in the observations x
returning initial information for MCEstimator used
by optimize resp. optim; i.e; if (total) parameter is of
length 1, startPar returns a search interval, else it returns an initial
parameter value.
makeOKPar is a function in the (total)
parameter param; used if optim resp. optimize---
try to use ``illegal'' parameter values; then makeOKPar makes
a valid parameter value out of the illegal one; if NULL
slot makeOKPar of ParamFamily is used to produce it.
function: mapping from the parameter space
(represented by "param") to the distribution space
(represented by "distribution").
character vector: properties of the family
function: mapping from the parameter space (argument
param of class "ParamFamParameter") to a mapping from
observation x to the value of the L2derivative;
L2deriv.fct is used by modifyModel to
move the L2deriv according to a change in the parameter,
and to fill slot L2deriv.
More specifically, let us call the parts main and nuisance
of the parameter the unknown parameter. If this unknown parameter is
one-dimensional, the return value of L2deriv.fct must be a function
in argument x, which is vectorized, (i.e.,
callable for a vector-valued x), and has a one-dimensional, numeric
return value. In case the dimension of the unknown parameter is larger
than one, the return value must be a list of functions, each of which
satisfies the conditions formulated for the case of a one-dimensional
parameter of interest. The order of the components of this list is
the same as the order of the parameter coordinates in main, followed
by the ones in nuisance.
object of class "FunSymmList":
symmetry of the maps contained in L2deriv; a list
of symmetry properties of the same length as the return value of
L2deriv.fct .
object of class "UnivarDistrList":
distribution of L2deriv; the length of this list
of univariate distributions must be of the same length as the
return value of L2deriv.fct .
object of class "DistrSymmList":
symmetry of the distributions contained in L2derivDistr;
the length of this list of symmetry properties must be
of the same length as the return value of L2deriv.fct .
function: mapping from the parameter space (argument
param of class "ParamFamParameter") to the set of positive
semidefinite matrices; FisherInfo.fct is used by modifyModel to
move the Fisher information according to a change in the parameter
object of class "PosSemDefSymmMatrix":
Fisher information of the family
the class name of the return value; by default this
argument is NULL whereupon the return class will be
L2ParamFamily; but, internally, this generating function is also
used to e.g. produce objects of class BinomialFamily, PoisFamily
GammaFamily, BetaFamily.
logical of length 1: Tells R how to use the function from
slot startPar in case of a kStepEstimator---use it as is or
to compute the starting point for a minimum distance estimator which in
turn then serves as starting point for roptest / robest
(from package ROptEst). If TRUE (default) the latter
alternative is used. Ignored if ROptEst is not used.
Object of class "L2ParamFamily"
If name is missing, the default
“L2 differentiable parametric family of probability measures”
is used. In case distrSymm is missing it is set to
NoSymmetry().
If param is missing, the parameter is created via
main, nuisance and trafo as described
in ParamFamParameter. In case L2derivSymm is
missing, it is filled with an object of class FunSymmList
with entries NonSymmetric(). In case L2derivDistr is missing,
it is computed via imageDistr. If L2derivDistrSymm is missing,
it is set to an object of class DistrSymmList with entries
NoSymmetry(). In case FisherInfo is missing, it is computed
from L2deriv using E.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
# NOT RUN {
F1 <- L2ParamFamily()
plot(F1)
# }
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