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Adaptive greedy algorithm for moderately large dimensions in kernel conditional density estimation

Abstract : This paper studies the estimation of the conditional density f (x, ·) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) ∈ R d , i = 1,. .. , n. We assume that f depends only on r unknown components with typically r d. We provide an adaptive fully-nonparametric strategy based on kernel rules to estimate f. To select the bandwidth of our kernel rule, we propose a new fast iterative algorithm inspired by the Rodeo algorithm (Wasserman and Lafferty (2006)) to detect the sparsity structure of f. More precisely, in the minimax setting, our pointwise estimator, which is adaptive to both the regularity and the sparsity, achieves the quasi-optimal rate of convergence. Its computational complexity is only O(dn log n).
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02085677
Contributor : Vincent Rivoirard Connect in order to contact the contributor
Submitted on : Monday, June 28, 2021 - 1:01:43 PM
Last modification on : Sunday, June 26, 2022 - 10:06:48 AM

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  • HAL Id : hal-02085677, version 2
  • ARXIV : 2106.14669

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Minh-Lien Jeanne Nguyen, Claire Lacour, Vincent Rivoirard. Adaptive greedy algorithm for moderately large dimensions in kernel conditional density estimation. 2021. ⟨hal-02085677v2⟩

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