B1171
Title: Confidence sets for a level set in linear regression
Authors: Fang Wan - Lancaster University (United Kingdom) [presenting]
Wei Liu - University of Southampton (United Kingdom)
Frank Bretz - Novartis Pharma AG (Switzerland)
Abstract: Regression modelling is the workhorse of statistics, and there is vast literature on the estimation of the regression function. It is realized in recent years that in regression analysis, the ultimate aim may be the estimation of a level set of the regression function, instead of the estimation of the regression function itself. The published work on the estimation of the level set has thus far focused mainly on nonparametric regression, especially on point estimation. The construction of confidence sets for the level set of linear regression is considered. In particular, $1-\alpha$ level upper, lower and two-sided confidence sets are constructed for the normal-error linear regression. It is shown that these confidence sets can be easily constructed from the corresponding $1-\alpha$ level simultaneous confidence bands. It is also pointed out that the construction method is readily applicable to other parametric regression models where the mean response depends on a linear predictor through a monotonic link function, which includes generalized linear models, linear mixed models and generalized linear mixed models. Therefore the method is widely applicable. Examples are given to illustrate the method.
