Rectangular Confidence Regions and Prediction Regions in Multivariate Calibration

The multivariate calibration problem deals with inference concerning an unknown value of a covariate vector based on observation response vector. Two distinct scenarios are considered in the problem: controlled where covariates non-stochastic, and random random. Under calibration, interest is computation confidence region for that computing prediction Assuming standard normal linear regression model, rectangular regions derived using parametric bootstrap approach. Numerical results show accurately maintain coverage probabilities. illustrated examples. currently available literature all ellipsoidal, this work first attempt to derive regions.