We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.
AbstractIn this paper, we propose the r-d class predictors which are general predictors of the best linear unbiased predictor (BLUP), the principal components regression (PCR) and the Liu predictors in the linear mixed models.
Superiorities of the linear combination of the new predictors to each of these predictors are done in the sense of the mean square error matrix criterion.
Finally, numerical examples and a simulation study are done to illustrate the findings.
A matrix inequality and admissibility of linear estimators with respect to the mean square error matrix criterion