makeIC-methods: Generic Function for making ICs consistent at a possibly...

In RobAStBase: Robust Asymptotic Statistics

Generic Function for making ICs consistent at a possibly different model

Description

Generic function for providing centering and Fisher consistency of ICs.

Usage

makeIC(IC, L2Fam, ...)

## S4 method for signature 'IC,L2ParamFamily'
makeIC(IC, L2Fam, ..., diagnostic = FALSE)
## S4 method for signature 'list,L2ParamFamily'
makeIC(IC, L2Fam, forceIC = TRUE, name, Risks,
                  Infos, modifyIC = NULL, ..., diagnostic = FALSE)
## S4 method for signature 'function,L2ParamFamily'
makeIC(IC, L2Fam, forceIC = TRUE, name, 
                  Risks, Infos, modifyIC = NULL, ..., diagnostic = FALSE)

Arguments

IC	object of class "IC" for signature IC="IC", respectively a list of functions in one argument for signature IC="list", respectively a function in one argument for signature IC="function".
L2Fam	L2-differentiable family of probability measures; may be missing, in which case it is replaced by the family in slot CallL2Fam of IC.
forceIC	logical; shall centeredness and Fisher consistency be enforced applying an affine linear transformation?
name	Object of class "character"; the name of the IC
Risks	object of class "list": list of risks; cf. RiskType-class.
Infos	matrix of characters with two columns named method and message: additional informations.
modifyIC	object of class "OptionalFunction": function of four arguments: (1) L2Fam an L2 parametric family (2) IC an optional influence curve, (3) withMakeIC a logical argument whether to enforce the IC side conditions by makeIC, and (4) ... for arguments to be passed to calls to E in makeIC. Returns an object of class "IC". This function is mainly used for internal computations!
...	additional parameters to be passed to expectation E
diagnostic	logical; if TRUE, diagnostic information on the integration is printed and returned as attribute diagnostic of the return value.

Details

Argument IC is transformed affinely such that the transformed IC satisfies the defining side conditions of an IC, i.e., centeredness and Fisher consistency:

\mathop{\bm{E}}[{\rm IC}]=0

\mathop{\bm{E}}[{\rm IC}\,\Lambda^\tau]= D

where \Lambda is the L2 derivative of the model and D is the Jacobian of transformation trafo.

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.

Value

An IC of class "IC" at the model.

Methods

makeIC

signature(IC = "IC", L2Fam = "missing": creates an object of class "IC" at the parametric model of its own slot CallL2Fam; enforces IC conditions centeredness and Fisher consistency, applying an affine linear transformation.

makeIC

signature(IC = "IC", L2Fam = "L2ParamFamily": creates an object of class "IC" at the parametric model L2Fam; enforces IC conditions centeredness and Fisher consistency, applying an affine linear transformation.

makeIC

signature(IC = "list", L2Fam = "L2ParamFamily": creates an object of class "IC" out of a list of functions given by argument IC at the parametric model L2Fam; enforces IC conditions centeredness and Fisher consistency, applying an affine linear transformation.

makeIC

signature(IC = "function", L2Fam = "L2ParamFamily": creates an object of class "IC" out of a function given by argument IC at the parametric model L2Fam; enforces IC conditions centeredness and Fisher consistency, applying an affine linear transformation.

Author(s)

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-class, IC-class

Examples

## default IC
IC1 <- new("IC")

## L2-differentiable parametric family
B <- BinomFamily(13, 0.3)

## check IC properties
checkIC(IC1, B)

## make IC
IC2 <- makeIC(IC1, B)

## check IC properties
checkIC(IC2)

## slot modifyIC is filled in case of IC2
IC3 <- modifyIC(IC2)(BinomFamily(13, 0.2), IC2)
checkIC(IC3)
## identical to
checkIC(IC3, BinomFamily(13, 0.2))

IC4 <- makeIC(sin, B)
checkIC(IC4)

(IC5 <- makeIC(list(function(x)x^3), B, name="a try"))
plot(IC5)
checkIC(IC5)

## don't run to reduce check time on CRAN

N0 <- NormLocationScaleFamily()
IC6 <- makeIC(list(sin,cos),N0)
plot(IC6)
checkIC(IC6)

getRiskIC(IC6,risk=trAsCov())$trAsCov$value
getRiskIC(IC6,risk=asBias(),neighbor=ContNeighborhood())$asBias$value

RobAStBase documentation built on Jan. 12, 2025, 3:02 a.m.