Stepwise sampling procedure for estimating random averages
The aim of this Note is to present an optimal stepwise method for estimating an integral of a time series from observations at appropriately designed sampling points. Optimal linear estimators along with sampling points are constructed via a stepwise procedure. At each stage, one term is added to the existing estimator with the addition of one new sample, and previous observations and calculations are preserved. The stepwise method is also considered when simple linear nonparametric estimators are used. Asymptotically, an optimal one-step ahead sampling point is derived by maximizing an objective function that depends on the singularity of the process at the previous points.
Benhenni, Karim, and Yingcai Su. "Stepwise sampling procedure for estimating random averages." Comptes Rendus Mathematique 340, no. 8 (2005): 615-618.
Comptes Rendus Mathematique