The problem of constructing optimal confidence bands for a simple linear regression over the whole real line is considered. Optimality is defined as minimization of the average width of the bands weighted by a normalized function. This weight function is presented as an indicator of experimental interest in the varying width of the band. A comparison between the commonly seen hyperbolic bands and segmented-line bands is presented.
- Constrained minimization
- Prior weight functions
- Simultaneous confidence intervals
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty