Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region

This paper provides the method of constructing the simultaneous confidence band for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region. The band is compared with that on a rectangular region. It is shown that the band on the ellipsoidal region has a big advantage. The proposed method allows to construct the Type I band and the Type II band, and also allows to constrain the predictor variables either in finite intervals or in infinite intervals. In order to evaluate the efficiency of the band, the average width criterion is introduced, under which the Type I band and the Type II band are compared. All stated above are illustrated by a real example of a leaching rate study.