Locally best linear unbiased estimation of regression curves specified by nonlinear constraints on the model parameters

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00177016%3A_____%2F24%3AN0000138" target="_blank" >RIV/00177016:_____/24:N0000138 - isvavai.cz</a>

Result on the web

<a href="https://www.worldscientific.com/doi/abs/10.1142/9789819800674_0012" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/9789819800674_0012</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/9789819800674_0012" target="_blank" >10.1142/9789819800674_0012</a>

Result language

angličtina

Original language name

Locally best linear unbiased estimation of regression curves specified by nonlinear constraints on the model parameters

Original language description

This paper focuses on parameter estimation within the Errors-in-Variables (EIV) model with nonlinear constraints and the determination of associated uncertainties. This is motivated by a collaborative project in nanoscale material characterization, particularly the assessment of material properties like hardness and elasticity through instrumented indentation testing. Here we confront the challenge of precisely fitting curves specified by nonlinear constraints of the parameters to measurement results which come with associated uncertainties, while simultaneously managing their correlations. Such challenges are prevalent in numerous statistical and metrological applications. Our proposed approach is founded on iterative linearizations of the EIV model with nonlinear parameter constraints specified in implicit form, employing the Locally Best Linear Unbiased Estimation (LBLUE) method. LBLUE is a locally optimal technique known for providing an efficient and robust solution, particularly when dealing with weakly nonlinear models. We refer to this approach as the Optimum Estimate of Function Parameters by Iterated Linearization (OEFPIL). This method has been effectively implemented in various computing environments, including R and C, and is here introduced within the context of MATLAB, complete with illustrative examples. Compared to alternative estimation approaches in EIV models with nonlinear constraints, OEFPIL stands out for its simplicity, versatility, practicality, and computational efficiency, making it an excellent choice for applications in metrology and beyond.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/LUASK22008" target="_blank" >LUASK22008: Efficient computational methods for materials characterization at the nanoscale</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Advanced Mathematical and Computational Tools in Metrology and Testing XII

ISBN

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ISSN

1793-0901

e-ISSN

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Number of pages

8

Pages from-to

143-150

Publisher name

World Scientific

Place of publication

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Event location

Sarajevo

Event date

Sep 26, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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