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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/LUASK22008" target="_blank" >LUASK22008: Efektivní výpočetní metody pro charakterizaci materiálů v nanoměřítku</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

Advanced Mathematical and Computational Tools in Metrology and Testing XII

ISBN

—

ISSN

1793-0901

e-ISSN

—

Počet stran výsledku

8

Strana od-do

143-150

Název nakladatele

World Scientific

Místo vydání

—

Místo konání akce

Sarajevo

Datum konání akce

26. 9. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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