Efficient calibration of computer models with multivariate output

The classical calibration procedures of computer models only concern the univariate output, which would not be satisfied in practice. Multivariate output is gradually more prevalent in a wide range of real-world applications, which motivates us to develop a new calibration procedure to extend the classical calibration methods to multivariate cases. In this work, we propose an efficient calibration procedure for multivariate output within restricted correlation. First, we construct an estimator of the discrepancy function between the true process and the computer model by the local linear approximation, then obtain an estimator of the calibration parameter by the weighted profile least squares and establish its asymptotic properties. In addition, we also develop an estimator of the calibration parameter in a special situation, whose asymptotic normality has been derived. Numerical studies including simulations and an application to composite fuselage simulation verify the efficiency of the proposed calibration procedure.