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August 2021 Inference in a linear functional relationship with replications
Julio Hokama, Pedro Morettin, Heleno Bolfarine, Manuel Galea
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Braz. J. Probab. Stat. 35(3): 569-589 (August 2021). DOI: 10.1214/21-BJPS498


In this paper, we consider a model for data analysis with measurement errors. The main objective of this work is to develop statistical inference tools, such as parameter estimation and hypothesis tests in a linear functional relationship with replicated observations. For this purpose, we use the maximum likelihood method in the presence of incidental parameters, and the unbiased estimating equations approach. Both approaches lead to explicit expressions for the asymptotic covariance matrices of the estimators of the model parameters. A simulation study is performed to assess the empirical behavior of estimators and of a Wald statistic. The methodology is illustrated with a real data set.

Funding Statement

The authors acknowledge the partial financial support from Project Puente 001/2019 Direccción de Investigación de la Vicerrectoría de Investigación de la Pontificia Universidad Católica de Chile, Chile (MG), CNPq (JH) and Fapesp 2018/04654-9 (PM).


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Julio Hokama. Pedro Morettin. Heleno Bolfarine. Manuel Galea. "Inference in a linear functional relationship with replications." Braz. J. Probab. Stat. 35 (3) 569 - 589, August 2021.


Received: 1 October 2019; Accepted: 1 January 2021; Published: August 2021
First available in Project Euclid: 22 July 2021

Digital Object Identifier: 10.1214/21-BJPS498

Rights: Copyright © 2021 Brazilian Statistical Association


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Vol.35 • No. 3 • August 2021
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