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[inherited from class "ProbFamily"]
object of class "character":
name of the family.
distribution[inherited from class "ProbFamily"]
object of class "Distribution":
member of the family.
distrSymm[inherited from class "ProbFamily"]
object of class "DistributionSymmetry":
symmetry of distribution.
param[inherited from class "ParamFamily"]
object of class "ParamFamParameter":
parameter of the family.
fam.call[inherited from class "ParamFamily"]
object of class "call":
call by which parametric family was produced.
makeOKPar[inherited from class "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[inherited from class "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[inherited from class "ParamFamily"]
object of class "function":
mapping from the parameter space (represented by "param")
to the distribution space (represented by "distribution").
props[inherited from class "ProbFamily"]
object of class "character":
properties of the family.
L2derivobject of class "EuclRandVariable":
L2 derivative of the family. Its map slot must contain a list of functions.
Each function in this list must have just one argument x,
which is vectorized, (i.e., callable for a vector-valued x),
and has a one-dimensional, numeric return value.
L2deriv.fctobject of class "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.
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 "OptionalDistrListOrCall"
(i.e., NULL or an object of class "DistrList" or
the respective call to generate the latter object): if non-null
and non-call, a list which includes the 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 .
FisherInfo.fctobject of class "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
FisherInfoobject of class "PosDefSymmMatrix":
Fisher information of the family.
.withEvalL2derivDistrlogical of length one: if TRUE slot L2derivDistr gets
evaluated, otherwise it is only kept as call.
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. More precisely,
this method has arguments
plot(x, withSweave = getdistrOption("withSweave"),
main = FALSE, inner = TRUE, sub = FALSE,
col.inner = par("col.main"), cex.inner = 0.8,
bmar = par("mar")[1], tmar = par("mar")[3], ...,
mfColRow = TRUE, to.draw.arg = NULL, withSubst = TRUE)
where
object of class "L2ParamFamily"
logical: if TRUE (for working with Sweave)
no extra device is opened and height/width are not set
logical: is a main title to be used? or
just as argument main in plot.default.
logical: do panels have their own titles? or
character vector of / cast to length 'number of plotted
panels' with the corresponding panel titles. For further
information, see also
plot and the
description of argument main in plot.default.
logical: is a sub-title to be used? or
just as argument sub in plot.default.
top margin -- useful for non-standard main title sizes
bottom margin -- useful for non-standard sub title sizes
magnification to be used for inner titles relative
to the current setting of cex; as in
par; can be a vector of length 2; in this
case the first component is for the distribution panels, the
second for the L2-derivative-panels.
character or integer code; color for the inner title
shall default partition in panels be used ---
defaults to TRUE
Either NULL (default;
everything is plotted) or a vector of either integers
(the indices of the subplots to be drawn) or characters
--- the names of the subplots to be drawn: these
names are to be chosen among
c("d","p","q", dimnms) where dimnms is
either the row names of the trafo matrix
rownames(trafo(x@param)) or if the last expression
is NULL a vector "dim<dimnr>",
dimnr running through the number of rows of the
trafo matrix.
logical; if TRUE (default) pattern substitution for
titles and lables is used; otherwise no substitution is used.
addtional arguments for plot --- see
plot,
plot.default,
plot.stepfun
If ... contains argument ylim, this may either be
as in plot.default (i.e. a vector of length 2) or a vector of
length 4, where the first two elements are the values for ylim
in panels "d.c" and "d.d", and the last
two elements are the values for ylim resp. xlim in panels
"p", "p.c", "p.d" and "q", "q.c", "q.d".
In all title and axis label arguments, if withSubst is TRUE,
the following patterns are substituted:
"%C"class of argument x
"%A"deparsed argument x
"%D"time/date-string when the plot was generated
In addition, argument ... may contain arguments panel.first,
panel.last, i.e., hook expressions to be evaluated at the very beginning
and at the very end of each panel (within the then valid coordinates).
To be able to use these hooks for each panel individually, they may also be
lists of expressions (of the same length as the number of panels and
run through in the same order as the panels).
The return value of the plot methods is an S3 object of class
c("plotInfo","DiagnInfo"), i.e., a list
containing the information needed to produce the
respective plot, which at a later stage could be used by different
graphic engines (like, e.g. ggplot) to produce the plot
in a different framework. A more detailed description will follow in
a subsequent version.
signature(model = "L2ParamFamily", param = "ParamFamParameter"):
moves the L2-parametric Family model to parameter param
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
In the E-methods, diagnostics on the involved integrations are available
if argument diagnostic is TRUE. Then there is attribute
diagnostic attached to the return value, which may be inspected
and accessed through showDiagnostic and
getDiagnostic.
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)
## selection of subpanels for plotting
F2 <- L2LocationScaleFamily()
layout(matrix(c(1,2,3,3), nrow=2, byrow=TRUE))
plot(F2,mfColRow = FALSE,
to.draw.arg=c("p","q","loc"))
plot(F2,mfColRow = FALSE, inner=list("empirical cdf","pseudo-inverse",
"L2-deriv, loc.part"), to.draw.arg=c("p","q","loc"))
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