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\begin{document}

\title{Estimation of Output Measurement Variances for EVM Parameter Estimation}



\author[1]{Kaveh Abdi}%
\author[2]{Kimberley McAuley}%
\affil[1]{Queen's University Faculty of Engineering and Applied Science}%
\affil[2]{Queen's University}%


\vspace{-1em}



  
  \date{May 15, 2024}


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\begin{abstract}
Error-in-variables model (EVM) methods require information about input
and output measurement variances when estimating model parameters. In
EVM, using replicate experiments for estimating output measurement
variances is complicated, because true values of inputs may be different
when multiple attempts are made to repeat an experiment. To address this
issue, we categorize attempted replicate experiments as: i) true
replicates (TRs) when uncertain inputs are the same in replicated runs
and ii) pseudo-replicates (PRs) when measured inputs are the same, but
unknown true values of inputs are different. We propose methodologies to
obtain output measurement variance estimates and associated parameter
estimates for both situations. We also propose bootstrap methods for
obtaining joint-confidence information for the resulting parameter
estimates. A copolymerization case study is used to illustrate the
proposed techniques. We show that different assumptions noticeably
affect the uncertainties in the resulting reactivity-ratio estimates.%
\end{abstract}%



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