Critical values for uniform confidence bands for rqss fitting
Usage
critval(kappa, alpha = 0.05, rdf = 0)
Arguments
kappa
length of the tube
alpha
desired non-coverage of the band, intended coverage is 1 - alpha
rdf
"residual" degrees of freedom of the fitted object. If rdf=0
then the Gaussian version of the critical value is computed, otherwise
the value is based on standard Student t theory.
Details
The Hotelling tube approach to inference has a long and illustrious
history. See Johansen and Johnstone (1989) for an overview. The implementation
here is based on Sun and Loader (1994) and Loader's locfit package, although
a simpler root finding approach is substituted for the iterative method used
there. At this stage, only univariate bands may be constructed.
Value
A scalar critical value that acts as a multiplier for the uniform
confidence band construction.
References
Hotelling, H. (1939): “Tubes and Spheres in $n$-spaces, and a class
of statistical problems,” Am J. Math, 61, 440–460.
Johansen, S., I.M. Johnstone (1990): “Hotelling's
Theorem on the Volume of Tubes: Some Illustrations in Simultaneous
Inference and Data Analysis,” The Annals of Statistics, 18, 652–684.
Sun, J. and C.V. Loader: (1994) “Simultaneous Confidence Bands for Linear Regression
and smoothing,” The Annals of Statistics, 22, 1328–1345.