oneStepEstimator: Function for the computation of one-step estimates

Description

Function for the computation of one-step estimates.

Usage

oneStepEstimator(x, IC, start = NULL,
      useLast = getRobAStBaseOption("kStepUseLast"),
      withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
      IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
      na.rm = TRUE, startArgList = NULL, withMakeIC = FALSE, ...,
      E.argList = NULL)

Value

Object of class "kStepEstimate"

Arguments

x: sample
IC: object of class "InfluenceCurve"
start: initial estimate (for full parameter,i.e. in dimension \(k\) respective joint length of main and nuisance part of the parameter): either a numerical value, or an object of class "Estimate" or a function producing either a numerical value, or an object of class "Estimate" when evaluated at x,...; if missing or NULL, we use slot startPar of the L2family L2Fam from within IC.
useLast: which parameter estimate (initial estimate or one-step estimate) shall be used to fill the slots pIC, asvar and asbias of the return value.
withUpdateInKer: if there is a non-trivial trafo in the model with matrix \(D\), shall the parameter be updated on \({\rm ker}(D)\)?
IC.UpdateInKer: if there is a non-trivial trafo in the model with matrix \(D\), the IC to be used for this; if NULL the result of getboundedIC(L2Fam,D) is taken; this IC will then be projected onto \({\rm ker}(D)\).
na.rm: logical: if TRUE, the estimator is evaluated at complete.cases(x).
startArgList: a list of arguments to be given to argument start if the latter is a function; this list by default already starts with two unnamed items, the sample x, and the model eval(CallL2Fam(IC)); in case IC is not of class IC, the model argument L2Fam will be set to NULL.
withMakeIC: logical; if TRUE the [p]IC is passed through makeIC before return.
...: additional arguments
E.argList: NULL (default) or a named list of arguments to be passed to calls to E from kStepEstimator; potential clashes with arguments of the same name in ... are resolved by inserting the items of argument list E.argList as named items to the argument lists, so in case of collisions the item of E.argList overwrites the existing one from ....

Author

Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Details

Given an initial estimation start, a sample x and an influence curve IC the corresponding one-step estimator is computed.

In case IC is an object of class "IC" the slots asvar and asbias of the return value are filled (based on the initial estimate).

The default value of argument useLast is set by the global option kStepUseLast which by default is set to FALSE. In case of general models useLast remains unchanged during the computations. However, if slot CallL2Fam of IC generates an object of class "L2GroupParamFamily" the value of useLast is changed to TRUE. Explicitly setting useLast to TRUE should be done with care as in this situation the influence curve is re-computed using the value of the one-step estimate which may take quite a long time depending on the model.

If useLast is set to TRUE and slot modifyIC of IC is filled with some function (which can be used to re-compute the IC for a different parameter), the computation of asvar, asbias and IC is based on the one-step estimate.

References

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

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