RobAStBase (version 0.7.1)

kStepEstimator: Function for the computation of k-step estimates

Description

Function for the computation of k-step estimates.

Usage

kStepEstimator(x, IC, start = NULL, steps = 1L,
      useLast = getRobAStBaseOption("kStepUseLast"),
      withUpdateInKer = getRobAStBaseOption("withUpdateInKer"),
      IC.UpdateInKer = getRobAStBaseOption("IC.UpdateInKer"),
      withICList = getRobAStBaseOption("withICList"),
      withPICList = getRobAStBaseOption("withPICList"),
      na.rm = TRUE, startArgList = NULL, ...)

Arguments

x

sample

IC

object of class "IC"

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

steps

integer: number of steps

useLast

which parameter estimate (initial estimate or k-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)).

withPICList

logical: shall slot pICList of return value be filled?

withICList

logical: shall slot ICList of return value be filled?

...

additional parameters

Value

• Object of class "kStepEstimate".

concept

• k-step estimator
• estimator

Details

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

See Also

IC-class, kStepEstimate-class

Examples

if(require(ROptEst)){
## 1. generate a contaminated sample
ind <- rbinom(100, size=1, prob=0.05)
x <- rnorm(100, mean=0, sd=(1-ind) + ind*9)

## 2. Kolmogorov(-Smirnov) minimum distance estimator
(est0 <- MDEstimator(x=x, NormLocationScaleFamily()))

## 3. k-step estimation: radius known
N1 <- NormLocationScaleFamily(mean=estimate(est0)["mean"], sd=estimate(est0)["sd"])
N1.Rob <- InfRobModel(center = N1, neighbor = ContNeighborhood(radius = 0.5))
IC1 <- optIC(model = N1.Rob, risk = asMSE())
(est1 <- kStepEstimator(x, IC1, est0, steps = 3, withPIC = TRUE))
estimate(est1)
ksteps(est1)
pICList(est1)
start(est1)

## a transformed model
tfct <- function(x){
    nms0 <- c("mean","sd")
    nms  <- "comb"
    fval0 <- x[1]+2*x[2]
    names(fval0) <- nms
    mat0 <- matrix(c(1,2), nrow = 1, dimnames = list(nms,nms0))
    return(list(fval = fval0, mat = mat0))
}

N1.traf <- N1; trafo(N1.traf) <- tfct
N1R.traf <- N1.Rob; trafo(N1R.traf) <- tfct
IC1.traf <- optIC(model = N1R.traf, risk = asMSE())
(est0.traf <- MDEstimator(x, N1.traf))
(est1.traf <- kStepEstimator(x, IC1.traf, est0, steps = 3,
                withIC = TRUE, withPIC = TRUE, withUpdateInKer = FALSE))
(est1a.traf <- kStepEstimator(x, IC1.traf, est0, steps = 3,
                withIC = TRUE, withPIC = TRUE, withUpdateInKer = TRUE))
estimate(est1.traf)
ksteps(est1.traf)
pICList(est1.traf)
startval(est1.traf)

untransformed.estimate(est1.traf)
uksteps(est1.traf)
ICList(est1.traf)
ustartval(est1.traf)

estimate(est1a.traf)
ksteps(est1a.traf)
pICList(est1a.traf)
startval(est1a.traf)

untransformed.estimate(est1a.traf)
uksteps(est1a.traf)
ICList(est1a.traf)
ustartval(est1a.traf)
}