Design of experiments for simultaneous confidence bands
S3RI Member: Wei Liu
Collaborators: Tony Hayter (University of Denver),
Walter Piegorsch (University of Arizona)
Research Student: Pascal Ah-kine
Simultaneous confidence bands provide plausible ranges for regression models or for the differences between several regression models, and so are more intuitive and interpretable than hypothesis testing procedures widely used in regression analysis. They are increasingly used in practice, for example to make inferences in medical and pharmaceutical applications. An important challenge is the construction of a ‘good’ confidence band that allows the sharpest statistical inferences to be made. A common method used to assess and compare confidence bands is to apply the simple criterion of minimising the average band width.
In this EPSRC funded project we proposed a new criterion for comparing bands that seeks to minimise the area or volume of the confidence set for the coefficients of linear regression models associated with the bands. The research has identified the optimal confidence band under this criterion from within a family of confidence bands. It has also established that this band is often better than the usual hyperbolic or constant width confidence bands.
Current research is focussing on finding optimal designs under criteria related to simultaneous bands.
Outputs from this project include:
- Liu, W. and Hayter, A. J. (2007). Minimum area confidence set optimality for confidence bands in simple linear regression. Journal of the American Statistical Association, 102, 181-190.
- Liu, W., Hayter A.J., Piegorsch W. W. and Ah-kine, P. (2009). Journal of Multivariate Analysis, 100, 1432-1439.