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Wavelet Thresholding Estimation in a Poissonian Interactions Model with Application to Genomic Data

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  • Laure Sansonnet

Abstract

type="main" xml:id="sjos12009-abs-0001"> This paper deals with the study of dependencies between two given events modelled by point processes. In particular, we focus on the context of DNA to detect favoured or avoided distances between two given motifs along a genome suggesting possible interactions at a molecular level. For this, we naturally introduce a so-called reproduction function h that allows to quantify the favoured positions of the motifs and that is considered as the intensity of a Poisson process. Our first interest is the estimation of this function h assumed to be well localized. The estimator h ˜ based on random thresholds achieves an oracle inequality. Then, minimax properties of h ˜ on Besov balls B 2 , ∞ s ( R ) are established. Some simulations are provided, proving the good practical behaviour of our procedure. Finally, our method is applied to the analysis of the dependence between promoter sites and genes along the genome of the Escherichia coli bacterium.

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  • Laure Sansonnet, 2014. "Wavelet Thresholding Estimation in a Poissonian Interactions Model with Application to Genomic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 200-226, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:200-226
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    File URL: http://hdl.handle.net/10.1111/sjos.12009
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    References listed on IDEAS

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    1. Gusto Gaelle & Schbath Sophie, 2005. "FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-28, September.
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    Cited by:

    1. Martin Kroll, 2019. "Nonparametric intensity estimation from noisy observations of a Poisson process under unknown error distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 961-990, November.
    2. Gaëlle Chagny, 2015. "Adaptive Warped Kernel Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 336-360, June.

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