Optimal designs for series estimation in nonparametric regression with\n correlated data

2018/12/13 by Holger Dette, Dette, Holger, Maria Konstantinou +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1812.05553

openalex publication_date 2018/12/13 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the problem of designing experiments for series\nestimators in nonparametric regression models with correlated observations. We\nuse projection based estimators to derive an explicit solution of the best\nlinear oracle estimator in the continuous time model for all Markovian-type\nerror processes. These solutions are then used to construct estimators, which\ncan be calculated from the available data along with their corresponding\noptimal design points. Our results are illustrated by means of a simulation\nstudy, which demonstrates that the new series estimator has a better\nperformance than the commonly used techniques based on the optimal linear\nunbiased estimators. Moreover, we show that the performance of the estimators\nproposed in this paper can be further improved by choosing the design points\nappropriately.\n

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