  Identification of model parameters in computer simulations is an important
topic in computer experiments. We propose a new method, called the projected
kernel calibration method, to estimate these model parameters. The proposed
method is proven to be asymptotic normal and semi-parametric efficient. As a
frequentist method, the proposed method is as efficient as the $L_2$
calibration method proposed by Tuo and Wu [Ann. Statist. 43 (2015) 2331-2352].
On the other hand, the proposed method has a natural Bayesian version, which
the $L_2$ method does not have. This Bayesian version allows users to calculate
the credible region of the calibration parameters without using a large sample
approximation. We also show that, the inconsistency problem of the calibration
method proposed by Kennedy and O'Hagan [J. R. Stat. Soc. Ser. B. Stat.
Methodol. 63 (2001) 425-464] can be rectified by a simple modification of the
kernel matrix.
