Nonparametric simulation extrapolation for measurement‐error models

The presence of measurement error is a widespread issue, which, when ignored, can render the results an analysis unreliable. Numerous corrections for effects have been proposed and studied, often under assumption normally distributed, additive measurement-error model. In many situations, observed data are nonsymmetric, heavy-tailed, or otherwise highly non-normal. these settings, correction techniques relying on normality undesirable. We propose extension simulation extrapolation that nonparametric in sense no specific distributional assumptions required terms. technique be implemented either validation replicate measurements available, designed to immediately accessible those familiar with extrapolation. La présence d'erreurs de mesure constitue un problème courant dont la négligence risque d'affecter considérablement fiabilité des résultats obtenus lors d'une analyse. Diverses méthodes correctives ont été proposées et examinées afin tenir compte ces erreurs, souvent en supposant modèle additif d'erreur distribué selon une loi normale. Toutefois, dans nombreuses les données observées présentent asymétrie marquée, queues lourdes ou non-normalité prononcée. Il est donc inapproprié d'utiliser qui se fondent sur l'hypothèse normalité tels cas. Afin pallier cette problématique, auteurs ce travail développé l'approche d'extrapolation par simulation, présentant caractère non paramétrique ne requiert aucune hypothèse spécifique quant à distribution erreurs. Cette peut être mise œuvre lorsque mesures répétées sont disponibles veut aux praticiens familiers avec l'extrapolation simulation. Measurement error, where variate interest not accurately observed, pervasive issue undermine validity analysis. methods exist correct error. These commonly assume model distributed errors. This assumption, though appealing its simplicity, unreasonable real-world applications. See, instance, National Research Council (1986), Nusser al. (1996), Bollinger (1998), Purdom & Holmes (2005), McKenzie (2008), Xu, Kim Li (2017), Rajan Desai (2018). When made difficult test, such as regarding terms, concerns procedures amplified. accommodation non-normal errors therefore important area study. Nonparametric semiparametric methods, which do impose strict providing flexible ways error; see, Vuong Gorfine, Hsu Prentice (2004), Carroll (2006), Schennach Hu (2013), Yi (2017). addition several parametric developed account (Augustin, 2004; Koul Song, 2014). order facilitate errors, we present used (SIMEX) method (Cook Stefanski, 1994). Our does distributed. Instead, SIMEX procedure consistently corrects regardless refer standard P-SIMEX, SIMEX, distinguish it from our procedure, NP-SIMEX. It has shown P-SIMEX resilient deviations some settings Other authors non-normal, bias resulting substantial (Yi He, 2012; three-step consisting step, estimation step. step described remeasurement (Novick 2002), emphasizing P-SIMEX's similarities bootstrap procedures. Just by resampling empirical distribution, remeasuring using distribution. Doing so allows terms relaxed. make explicit this procedure. NP-SIMEX accommodate wide range models without making assumptions, distinguishes extensions Laplace (Koul Suppose sample indexed i ∈ { 1 , … n } . take Y represent outcome interest, X explanatory variable subject Z vector variables measured taken univariate ease notation. concerned estimating parameter θ relates Instead observing observe ∗ = + U term, independent that, error-free setting, estimator ^ ( ) consistent Generally, measurement-error-correction rely auxiliary infer information about Validation data, internal external, involve observation true alongside proxy set individuals. Internal arise situation subset taken. That is, total observations, while only remainder sample. External setting where, inside measured, but pairs separate dataset. use external must transportability models. process equivalent within interest. us If if