# Optimal designs for series estimation in nonparametric regression with correlated data

## TL;DR

This paper develops optimal experimental designs for series estimators in nonparametric regression with correlated data, improving estimator performance through explicit solutions and optimal design point selection.

## Contribution

It provides explicit solutions for the best linear oracle estimator in continuous time for Markovian error processes and introduces data-driven estimators with optimized design points.

## Key findings

- New series estimator outperforms traditional methods
- Optimal design points enhance estimator accuracy
- Simulation confirms improved performance

## 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.