Optimal designs for series estimation in nonparametric regression with correlated data

Abstract

In this paper 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 new series estimator has a better performance than the commonly used techniques based on the optimal linear unbiased estimators. Moreover, we show that the performance of the estimators proposed in this paper can be further improved by choosing the design points appropriately.

Minimax D-optimal designs for multivariate regression models with multi-factors

“…Another body of work investigated optimal designs under continuous time regression models with correlated errors (Dette et al 2016, Dette, Konstantinou & Zhigljavsky 2017, Dette, Schorning & Konstantinou 2017, Dette et al 2018, including continuous time versions of model ( 1)-(…”