Optimal designs for series estimation in nonparametric regression with correlated data

Schorning, K. and Konstantinou, M. and Dette, H.

Volume: 31 Pages: 1643-1667
DOI: 10.5705/ss.202018.0497
Published: 2021

We investigate the problem of designing experiments for series estimators in nonparametric regression models with correlated observations. We use projection-based estimators to derive an explicit solution of the best linear oracle estimator in the continuous-time model for all Markovian-type error processes. These solutions are then used to construct estimators, which can be calculated from the available data, along with their corresponding optimal design points. Our results are illustrated by means of a simulation study, which demonstrates that the proposed series estimator outperforms commonly used techniques based on the optimal linear unbiased estimators. Moreover, we show that the performance of the proposed estimators can be further improved by choosing the design points appropriately. © 2021 Institute of Statistical Science. All rights reserved.

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