On deconvolution with repeated measurements

Delaigle, Aurore; Hall, Peter; Meister, Alexander

doi:10.1214/009053607000000884

Cited by 164 publications

(171 citation statements)

References 29 publications

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“…Since assuming ε symmetric is equivalent to assuming f * ε real-valued, we can see that (A1) is equivalent to the assumption 2.2 in Delaigle et al [2008]. Therefore, Assumption (A1) implies that ∀t ∈ R, f * ε (t) ∈ R * + .…”

Section: Assumption(a1)mentioning

confidence: 99%

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Deconvolution Estimation of Onset of Pregnancy with Replicate Observations

Comte

Samson

Stirnemann

2013

Scandinavian J Statistics

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To cite this version:Fabienne Comte, Adeline Samson, Julien Stirnemann. Deconvolution estimation of onset of pregnancy with replicate observations. Scandinavian Journal of Statistics, Wiley, 2014, 41 (2) Abstract. In general, the precise date of onset of pregnancy is unknown and may only be estimated from ultrasound biometric measurements of the embryo. We want to estimate the density of the random variables corresponding to the interval between last menstrual period and true onset of pregnancy. The observations correspond to the variables of interest up to an additive noise. We suggest an estimation procedure based on deconvolution. It requires the knowledge of the density of the noise which is not available. But we have at our disposal another specific sample with replicate observations for twin pregnancies. This allows both to estimate the noise density and to improve the deconvolution step. Convergence rates of the final estimator are studied and compared to other settings. Our estimator involves a cut-off parameter for which we propose a cross-validation type procedure. Lastly, we estimate the target density in spontaneous pregnancies with an estimation of the noise obtained from replicate observations in twin pregnancies.En général, la date précise de début de grossesse est inconnue et est seulement estiméeà partir de mesures de l'embryon par ultrasons. Nous voulons estimer la densité de la variable aléatoire correspondantà l'intervalle entre la date des dernières règles et le début réel de la grossesse. Les observations dont nous disposons correspondent aux variables d'intérêt mesurées avec un bruit additif. Nous proposons une procédure d'estimation basée sur des techniques de déconvolution. Cela requiert la connaissance de la loi du bruit mais elle n'est pas disponible. En revanche, nous disposons d'unéchantillon d'observations répétées obtenuesà partir de grossesses gémellaires. Cela nous permetà la fois d'estimer la loi du bruit et d'améliorer la procédure de déconvolution. La vitesse de convergence de l'estimateur résultant estétudiée et comparéeà celles obtenues dans d'autres contextes. Notre estimateur contient un paramètre de troncature pour lequel nous proposons une sélection par validation croisée. Pour finir, nousétudions notre estimateur en simulation puis nous l'appliquons pour estimer la densité visée sur notré echantillon de grossesses spontanées avec estimation du bruit via des données répétées obtenues sur unéchantillon de grossesses gémellaires.

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Section: Assumption(a1)mentioning

confidence: 99%

“…Therefore, given that E e it(ε −j1 −ε −j2 ) = E e it(Y −j1 −Y −j2 ) and under the hypothesis (A1), Delaigle et al [2008] propose the following estimator of (f * ε )…”

Section: Assumption(a1)mentioning

confidence: 99%

Deconvolution Estimation of Onset of Pregnancy with Replicate Observations

Comte

Samson

Stirnemann

2013

Scandinavian J Statistics

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“…of  * in a simpler way (see Markatou (1996), Li andVuong (1998), Delaigle, Hall, and Meister (2008)) by noting that…”

Section: Repeated Measurementsmentioning

confidence: 99%

Measurement error in nonlinear models - a review

Schennach¹

2012

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This overview of the recent econometrics literature on measurement error in nonlinear models centers on the question of the identification and estimation of general nonlinear models with measurement error. Simple approaches that rely on distributional knowledge regarding the measurement error (such as deconvolution or validation data techniques) are briefly presented.Then follows a description of methods that secure identification via more readily available auxiliary variables (such as repeated measurements, measurement systems with a "factor model" structure, instrumental variables and panel data). Methods exploiting higher-order moments or bounding techniques to avoid the need for auxiliary information are presented next. Special attention is devoted to a recently introduced general method to handle a broad class of latent variable models, called Entropic Latent Variable Integration via Simulation (ELVIS). Finally, the complex but active topic of nonclassical measurement error is covered and applications of measurement error techniques to other fields are outlined.

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“…In Carroll and Hall (1988) he provided the minimax rate of convergence for nonparametric density estimation. In Delaigle, Hall and Meister (2008), Peter studied the problem in case the density of U is unknown but is estimated from repeated contaminated measurements. Recently, in his last paper on the topic (Delaigle and Hall, 2016), he demonstrated that one may estimate the density of X using its phase function.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Errors-in-Variables Partially Linear Additive Models

Park¹,

Lee²,

Han³

2018

STAT SINICA

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In this paper we consider partially linear additive models where the predictors in the parametric and in the nonparametric parts are contaminated by measurement errors. We propose an estimator of the parametric part and show that it achieves √ n-consistency in a certain range of the smoothness of the measurement errors in the nonparametric part. We also derive the convergence rate of the parametric estimator in case the smoothness of the measurement errors is off the range. Furthermore, we suggest an estimator of the additive function in the nonparametric part that achieves the optimal one-dimensional convergence rate in nonparametric deconvolution problems. We conducted a simulation study that confirms our theoretical findings.

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On deconvolution with repeated measurements

Cited by 164 publications

References 29 publications

Deconvolution Estimation of Onset of Pregnancy with Replicate Observations

Deconvolution Estimation of Onset of Pregnancy with Replicate Observations

Measurement error in nonlinear models - a review

Estimation of Errors-in-Variables Partially Linear Additive Models

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