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August 2019 The BLUE in continuous-time regression models with correlated errors
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
Ann. Statist. 47(4): 1928-1959 (August 2019). DOI: 10.1214/18-AOS1734


In this paper, the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressive errors of order two and integrated error processes (such as integrated Brownian motion). The results are illustrated on many examples.


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Holger Dette. Andrey Pepelyshev. Anatoly Zhigljavsky. "The BLUE in continuous-time regression models with correlated errors." Ann. Statist. 47 (4) 1928 - 1959, August 2019.


Received: 1 October 2017; Revised: 1 May 2018; Published: August 2019
First available in Project Euclid: 21 May 2019

zbMATH: 07082275
MathSciNet: MR3953440
Digital Object Identifier: 10.1214/18-AOS1734

Primary: 62M10
Secondary: 62M09

Keywords: AR processes , BLUE , continuous autoregressive model , correlated observations , Linear regression , optimal design , signed measures

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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