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")
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psi |
Number or vector. Takes value(s) in interval 0,1. |
ref.dist |
Character. Reference distribution
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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 <bent.nielsen@nuffield.ox.ac.uk> 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,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))
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