# Adaptive estimation of the conditional density in presence of censoring.

Abstract : Consider an i.i.d. sample $(X_i,Y_i)$, $i=1, \dots, n$ of observations and denote by $\pi(x,y)$ the conditional density of $Y_i$ given $X_i=x$. We provide an adaptive nonparametric strategy to estimate $\pi$. We prove that our estimator realizes a global squared-bias/variance compromise in a context of anisotropic function classes. We prove that our procedure can be adapted to positive censored random variables $Y_i$'s, i.e. when only $Z_i=\inf(Y_i, C_i)$ and $\delta_i=\1_{\{Y_i\leq C_i\}}$ are observed, for an i.i.d. censoring sequence $(C_i)_{1\leq i\leq n}$ independent of $(X_i,Y_i)_{1\leq i\leq n}$. Simulation experiments illustrate the method.
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Journal articles
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Cited literature [18 references]

https://hal.archives-ouvertes.fr/hal-00152794
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Submitted on : Thursday, June 7, 2007 - 8:48:45 PM
Last modification on : Saturday, March 26, 2022 - 4:12:47 AM
Long-term archiving on: : Monday, June 27, 2011 - 4:18:30 PM

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• HAL Id : hal-00152794, version 1

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Elodie Brunel, Fabienne Comte, Claire Lacour. Adaptive estimation of the conditional density in presence of censoring.. Sankhya: The Indian Journal of Statistics, Indian Statistical Institute, 2007, 69 (Part 4.), p. 734-763. ⟨hal-00152794⟩

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