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Deconvolution Estimation of Onset of Pregnancy with Replicate Observations

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  • Fabienne Comte
  • Adeline Samson
  • Julien J Stirnemann

Abstract

type="main" xml:id="sjos12029-abs-0001"> 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 with 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.

Suggested Citation

  • Fabienne Comte & Adeline Samson & Julien J Stirnemann, 2014. "Deconvolution Estimation of Onset of Pregnancy with Replicate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 325-345, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:325-345
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    File URL: http://hdl.handle.net/10.1111/sjos.12029
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    References listed on IDEAS

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    1. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 19-47, March.
    2. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    3. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, September.
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    1. Comte, Fabienne & Kappus, Johanna, 2015. "Density deconvolution from repeated measurements without symmetry assumption on the errors," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 31-46.
    2. Van Ha Hoang & Thanh Mai Pham Ngoc & Vincent Rivoirard & Viet Chi Tran, 2022. "Nonparametric estimation of the fragmentation kernel based on a partial differential equation stationary distribution approximation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 4-43, March.

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