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)