Add confidence interval

Add a confidence interval to a spectral estimate assuming the uncertainty of the spectral estimates follows a chi-squared distribution with the degrees of the freedom from the spectral estimates.

Usage

AddConfInterval(spec, pval = 0.05, MINVALUE = 1e-10)

Arguments

spec

a spectral object of class "spec" or a list with the minimum components spec and dof which are vectors of the same length giving the spectral estimates and the corresponding degrees of freedom.

pval

numeric; p value for the confidence interval, i.e. the interval is constructed from pval / 2 to 1 - pval / 2.

MINVALUE

numeric; minimum value to limit the confidence interval.

Value

the input object including the new list elements lim.1 and

lim.2 giving the upper and lower bound of the confidence interval, respectively.

Author

Thomas Laepple

Examples

N.R <- 1000
N.T <- 100
save.spec <- matrix(NA, N.T / 2, N.R)
for (i.R in 1 : N.R) {
  save.spec[, i.R] <- SpecMTM(ts(SimPowerlaw(1, N.T)))$spec
}

q.empirical <- apply(save.spec, 1, quantile, c(0.025, 0.975))
testspec <- SpecMTM(ts(SimPowerlaw(1, N.T)))

LPlot(AddConfInterval(testspec), ylim = c(0.05, 10))
lines(testspec$freq, q.empirical[1, ], col = "red")
lines(testspec$freq, q.empirical[2, ],col = "red")
legend("bottomleft", lwd = 2, col = c("black", "red"),
       legend = c("one realization with chisq conf intervals",
                  "MC confidence intervals"))