Generalized formulation of extended cross-section adjustment method based on minimum variance unbiased linear estimation

By introducing a new assumption of linear estimation, we derive a new formulation of the extended cross-section adjustment (EA) method, which minimizes the variance of the design target core parameters. The new formulation is derived on the basis of minimum variance unbiased estimation with no use of the assumption of normal distribution. In this formulation, we found that EA has infinitely many solutions as the adjusted cross-section set. The new formulation of EA can represent all the possible solutions minimizing the variance of the design target core parameters and includes a special case identical to the classical Bayesian EA method, which was derived on the basis of the Bayes theorem under the assumption of normal distribution. Moreover, we prove that the special case minimizes not only the variance of the design target core parameters but also the variance of the nuclear data. Meanwhile, we show that the new assumption of linear estimation is consistent with the Kalman filter and demonstrate that we can formulate similarly the extended bias factor method, the conventional cross-section adjustment method, and the regressive cross-section adjustment method with no use of the assumption of normal distribution. (author)