Description Usage Arguments Details Value Author(s) References Examples
View source: R/ForwardSearch.r
Computes functions appearing in asymptotic theory of Forward Search based on Johansen and Nielsen (2013).
1  ForwardSearch.pointwise.asymptotics(psi, ref.dist = "normal")

psi 
Number or vector. Takes value(s) in interval 0,1. 
ref.dist 
Character. Reference distribution

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.
varpi 
Number or vector. sdv for forward residuals normalized by variance estimator and multiplied by twice the reference densisty. 
zeta 
Number or vector. Consistency correction factor. 
sdv.unbiased 
Number or vector. varpi/2/f. 
sdv.biased 
Number or vector. varpi/2/f/zeta. 
c 
Number or vector. c (median in unbiased case). 
median.biased 
Number or vector. median (in biased case). 
Bent Nielsen <[email protected]> 9 Sep 2014
Johansen, S. and Nielsen, B. (2013) Asymptotic analysis of the Forward Search. Download: Nuffield DP.
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# EXAMPLE 1
# Suppose n=100. Get asymptotic values for grid psi = (1, ... ,n)/n
n < 100
psi < seq(1,n1)/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.biased2*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$c2*FS$sdv.unbiased/sqrt(n))
lines(psi,FS$c+2*FS$sdv.unbiased/sqrt(n))

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