An Improved Approach to Multivariate Linear Calibration [Mathematics Subject Classification 62P25]


1 Faculty of Administrative Sciences, Air University, E-9, Islamabad Pakistan

2 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia


The article presents an approach to multivariate linear calibration based on the best linear predictor. The bias and mean squared error for the suggested predictor are derived in order to examine its properties. It has been examined that Bias/ and MSE/ are function of five invariant quantities. A simulation study is made for different values of response variables and sample sizes assuming different distributions for the explanatory variable. It is observed that the proposed estimator performs quite well. Some approximations to mean squared error have been suggested and the pivotal functions based on these approximations have been defined. Lower and upper tail probabilities have been calculated and it is examined that these are quite reasonable. These probabilities suggest that the relevant intervals have sensible confidence coefficient. Moreover, it is also shown that the multivariate classical and inverse estimators are special cases of the proposed estimator.