We study the computational complexity and variance of multilevel best linear unbiased estimators introduced in [D. Schaden E. Ullmann, SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 601--635]. specialize results this work to PDE-based models that are parameterized by a discretization quantity, e.g., finite element mesh size. In particular, we investigate asymptotic so-called sample allocation o...

For any given central moving-average trend filter, a family of end filters is constructed using a minimum revisions criterion and a local dynamic model operating within the span of the central filter. These end filters are equivalent to evaluating the central filter with unknown observations replaced by constrained optimal linear predictors. Two prediction methods are considered. Best Linear Un...

In this contribution, we extend the existing theory of minimummean squared error prediction (best prediction). This extention is motivated by the desire to be able to deal with models in which the parameter vectors have real-valued and/or integer-valued entries. New classes of predictors are introduced, based on the principle of equivariance. Equivariant prediction is developed for the real-par...

Predictions for the rate of inbreeding (DeltaF) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expe...