| L2ParamFamily-class {distrMod} | R Documentation |
Class of L2 differentiable parametric families.
Objects can be created by calls of the form new("L2ParamFamily", ...).
More frequently they are created via the generating function
L2ParamFamily.
name:"ProbFamily"]
object of class "character":
name of the family. distribution:"ProbFamily"]
object of class "Distribution":
member of the family. distrSymm:"ProbFamily"]
object of class "DistributionSymmetry":
symmetry of distribution. param:"ParamFamily"]
object of class "ParamFamParameter":
parameter of the family. fam.call:"ParamFamily"]
object of class "call":
call by which parametric family was produced.makeOKPar:"ParamFamily"]
object of class "function":
has argument param — the (total) parameter,
returns valid parameter; used if optim resp. optimize—
try to use ``illegal'' parameter values; then makeOKPar makes
a valid parameter value out of the illegal one.startPar:"ParamFamily"]
object of class "function":
has argument x — the data,
returns starting parameter for optim resp. optimize—
a starting estimator in case parameter is multivariate
or a search interval in case parameter is univariate.modifyParam:"ParamFamily"]
object of class "function":
mapping from the parameter space (represented by "param")
to the distribution space (represented by "distribution"). props:"ProbFamily"]
object of class "character":
properties of the family. L2deriv:"EuclRandVariable":
L2 derivative of the family. L2deriv.fct:"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 then used from observation
x to value of the L2derivative; L2deriv.fct is used by
modifyModel to move the L2deriv according to a change in the
parameter L2derivSymm:"FunSymmList":
symmetry of the maps included in L2deriv. L2derivDistr:"UnivarDistrList":
list which includes the distribution of L2deriv. L2derivDistrSymm:"DistrSymmList":
symmetry of the distributions included in L2derivDistr. FisherInfo.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 FisherInfo:"PosDefSymmMatrix":
Fisher information of the family.
Class "ParamFamily", directly.
Class "ProbFamily", by class "ParamFamily".
signature(object = "L2ParamFamily"):
accessor function for L2deriv. signature(object = "L2ParamFamily",
param = "ParamFamParameter"):
returns the L2derivative at param, i.e.
evaluates slot function L2deriv.fct at param. signature(object = "L2ParamFamily"):
accessor function for L2derivSymm. signature(object = "L2ParamFamily"):
accessor function for L2derivDistr. signature(object = "L2ParamFamily"):
accessor function for L2derivDistrSymm. signature(object = "L2ParamFamily"):
accessor function for FisherInfo. signature(object = "L2ParamFamily",
param = "ParamFamParameter"):
returns the Fisher Information at param, i.e.
evaluates slot function FisherInfo.fct at param. signature(object = "L2ParamFamily"):
check centering of L2deriv and compute precision
of Fisher information. signature(object = "L2ParamFamily", fun = "EuclRandVariable", cond = "missing"):
expectation of fun under the distribution of object. signature(object = "L2ParamFamily", fun = "EuclRandMatrix", cond = "missing"):
expectation of fun under the distribution of object. signature(object = "L2ParamFamily", fun = "EuclRandVarList", cond = "missing"):
expectation of fun under the distribution of object. signature(x = "L2ParamFamily"):
plot of distribution and L2deriv. signature(model = "L2ParamFamily", param = "ParamFamParameter"):
moves the L2-parametric Family model to parameter param
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ParamFamily, ParamFamily-class
F1 <- new("L2ParamFamily")
plot(F1)