Functions for asymptotic theory of Forward Search

Description

Computes functions appearing in asymptotic theory of Forward Search based on Johansen and Nielsen (2013).

Usage

ForwardSearch.pointwise.asymptotics(psi, ref.dist = "normal")

Arguments

Details

The asymptotic theory is developed in Johansen and Nielsen (2013), see Section 2.2.

c and ψ are linked through P(|ε|<c)=ψ, where ε is a random variable with the chosen reference distribution.

ζ is a consistency factor. Its square is defined as the truncated second moment τ = int_{-c}^{c} x^2 f(x) dx divided by ψ.

varpi is the asymptotic standard deviation resulting from Theorem 3.3.

Value

Author(s)

Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 9 Sep 2014

References

Johansen, S. and Nielsen, B. (2013) Asymptotic analysis of the Forward Search. Download: Nuffield DP.

Examples

#####################
#	EXAMPLE 1
#	Suppose n=100. Get asymptotic values for grid psi = (1, ... ,n)/n

n	<- 100
psi	<- seq(1,n-1)/n
FS	<- ForwardSearch.pointwise.asymptotics(psi)

#	Plot for biased normalisation
#	- matching choice of Atkinson and Riani (2000)

main <- "Pointwise confidence bands for n=100\n Biased normalisation"
ylab <-	"forward residual asymptotics"
 plot(psi,FS$median.biased,ylim=c(0,3),ylab=ylab,main=main,type="l")
lines(psi,FS$median.biased-2*FS$sdv.biased/sqrt(n))
lines(psi,FS$median.biased+2*FS$sdv.biased/sqrt(n))

#	Plot for unbiased normalisation

main <- "Pointwise confidence bands for n=100\n Unbiased normalisation"
ylab <-	"forward residual asymptotics"
 plot(psi,FS$c,ylim=c(0,3),ylab=ylab,main=main,type="l")
lines(psi,FS$c-2*FS$sdv.unbiased/sqrt(n))
lines(psi,FS$c+2*FS$sdv.unbiased/sqrt(n))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(ForwardSearch)
Loading required package: robustbase
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ForwardSearch/ForwardSearch.pointwise.asymptotics.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ForwardSearch.pointwise.asymptotics
> ### Title: Functions for asymptotic theory of Forward Search
> ### Aliases: ForwardSearch.pointwise.asymptotics
> 
> ### ** Examples
> 
> #####################
> #	EXAMPLE 1
> #	Suppose n=100. Get asymptotic values for grid psi = (1, ... ,n)/n
> 
> n	<- 100
> psi	<- seq(1,n-1)/n
> FS	<- ForwardSearch.pointwise.asymptotics(psi)
> 
> #	Plot for biased normalisation
> #	- matching choice of Atkinson and Riani (2000)
> 
> main <- "Pointwise confidence bands for n=100\n Biased normalisation"
> ylab <-	"forward residual asymptotics"
>  plot(psi,FS$median.biased,ylim=c(0,3),ylab=ylab,main=main,type="l")
> lines(psi,FS$median.biased-2*FS$sdv.biased/sqrt(n))
> lines(psi,FS$median.biased+2*FS$sdv.biased/sqrt(n))
> 
> #	Plot for unbiased normalisation
> 
> main <- "Pointwise confidence bands for n=100\n Unbiased normalisation"
> ylab <-	"forward residual asymptotics"
>  plot(psi,FS$c,ylim=c(0,3),ylab=ylab,main=main,type="l")
> lines(psi,FS$c-2*FS$sdv.unbiased/sqrt(n))
> lines(psi,FS$c+2*FS$sdv.unbiased/sqrt(n))
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>