psd (version 0.4-1)

spec_confint: Multitaper PSD confidence intervals.

Description

Multitaper PSD confidence intervals.

Usage

spec_confint(dof, p = 0.95, as.db = FALSE)
## S3 method for class 'spec':
spec_confint(dof, p = 0.95, as.db = FALSE)
## S3 method for class 'tapers':
spec_confint(dof, p = 0.95, as.db = FALSE)
## S3 method for class 'default':
spec_confint(dof, p = 0.95, as.db = FALSE)

Arguments

dof

numeric; the degrees of freedom $\nu$

p

numeric; the coverage probability $p$, bound within $[0,1)$

as.db

logical; should the values be returned as decibels?

Value

• A data.frame with the following properties (and names):
  • lower: Based on upper tail probabilities ($p$)
• upper: Based on lower tail probabilities ($1-p$)
• median: Based on lower tail probabilities ($p=0.5$)
• approx: Approximation based on $1/\sqrt(\nu - 1)$.

Details

The errors are estimated from the number of degrees of freedom $\nu$ by evaluating the $\chi_{p,\nu}^{2}(\nu,\nu)$ distribution for an optional coverage probability $p$ (defaulting to $p=0.95$). Additionally, the $p=0.5$ values and an approximation from $1/\sqrt{\nu - 1}$ are returned.

A more sophisticated (and complicated) approach would be to estimate via jack-knifing (Prieto et al 2007), but this is not yet made available.

Additive uncertainties $\delta S$ are returned, such that the spectrum with confidence interval is $S \pm \delta S$.

See Also

spectral_properties, psd-package, plot.spec, dB

Examples

#RDEX#\dontrun{
require(psd)
##
## Confidence intervals from taper numbers
##
sp <- spectral_properties(as.tapers(1:50), p=0.95, db.ci=TRUE)
par(las=1)
plot(stderr.chi.upper ~ taper, sp, type="s",
       ylim=c(-10,20), yaxs="i", xaxs="i",
       xlab=expression("number of tapers ("* nu/2 *")"), ylab="dB",
       main="Spectral uncertainties")
mtext("(additive factor)", line=.3)
lines(stderr.chi.lower ~ taper, sp, type="s")
lines(stderr.chi.median ~ taper, sp, type="s", lwd=2)
lines(stderr.chi.approx ~ taper, sp, type="s", col="red",lwd=2)
# to reach 3 db width confidence interval at p=.95
abline(v=33, lty=3)
legend("topright",
        c(expression("Based on "* chi^2 *"(p,"*nu*") and (1-p,"*nu*")"),
          expression(""* chi^2 *"(p=0.5,"*nu*")"),
          "approximation"),
lwd=c(1,3,3), col=c("black","black","red"), bg="white")
##
#RDEX#}