A note on optimal joint prediction of order statistics

The problem of prediction of several future order statistics, based on previous ones, is considered. An optimal predictor is defined as one minimizing the determinant of the covariance matrix of the predictor or of the predictive error vector. It is shown that the Lagrange multipliers method works well in all cases, despite some statements in the papers by Balakrishnan et al. [Metrika 85 (2022), 253–267; J. Multivariate Anal. 188 (2022), art. 104854; Statistics 57 (2023), 1239–1250].