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)
Object of class "L2ParamFamily"
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.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
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.
L2ParamFamily-class
F1 <- L2ParamFamily()
plot(F1)
Run the code above in your browser using DataLab