L2ParamFamily-class {distrMod}

L2 differentiable parametric family

Description

Class of L2 differentiable parametric families.

Details

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.

Objects from the Class

Objects can be created by calls of the form new("L2ParamFamily", ...). More frequently they are created via the generating function L2ParamFamily.

Slots

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.

L2deriv

object 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.fct

object 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.

L2derivSymm

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 .

L2derivDistr

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 .

L2derivDistrSymm

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.fct

object 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

FisherInfo

object of class "PosDefSymmMatrix": Fisher information of the family.

.withEvalL2derivDistr

logical of length one: if TRUE slot L2derivDistr gets evaluated, otherwise it is only kept as call.

Extends

Class "ParamFamily", directly.
Class "ProbFamily", by class "ParamFamily".

Methods

L2deriv

signature(object = "L2ParamFamily"): accessor function for L2deriv.

L2deriv

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the L2derivative at param, i.e. evaluates slot function L2deriv.fct at param.

L2derivSymm

signature(object = "L2ParamFamily"): accessor function for L2derivSymm.

L2derivDistr

signature(object = "L2ParamFamily"): accessor function for L2derivDistr.

L2derivDistrSymm

signature(object = "L2ParamFamily"): accessor function for L2derivDistrSymm.

FisherInfo

signature(object = "L2ParamFamily"): accessor function for FisherInfo.

FisherInfo

signature(object = "L2ParamFamily", param = "ParamFamParameter"): returns the Fisher Information at param, i.e. evaluates slot function FisherInfo.fct at param.

checkL2deriv

signature(object = "L2ParamFamily"): check centering of L2deriv and compute precision of Fisher information.

E

signature(object = "L2ParamFamily", fun = "EuclRandVariable", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandMatrix", cond = "missing"): expectation of fun under the distribution of object.

E

signature(object = "L2ParamFamily", fun = "EuclRandVarList", cond = "missing"): expectation of fun under the distribution of object.

plot

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

x

object of class "L2ParamFamily"

withSweave

logical: if TRUE (for working with Sweave) no extra device is opened and height/width are not set

main

logical: is a main title to be used? or
just as argument main in plot.default.

inner

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.

sub

logical: is a sub-title to be used? or
just as argument sub in plot.default.

tmar

top margin – useful for non-standard main title sizes

bmar

bottom margin – useful for non-standard sub title sizes

cex.inner

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.

col.inner

character or integer code; color for the inner title

mfColRow

shall default partition in panels be used — defaults to TRUE

to.draw.arg

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.

withSubst

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.

modifyModel

signature(model = "L2ParamFamily", param = "ParamFamParameter"): moves the L2-parametric Family model to parameter param

Author(s)

Matthias Kohl [e-mail],
Peter Ruckdeschel [e-mail]

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

See Also

L2ParamFamily, ParamFamily-class

Examples

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"))