Non compact estimation of the conditional density from direct or noisy data

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2023-08-01 DOI:10.1214/22-aihp1291
F. Comte, C. Lacour
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引用次数: 2

Abstract

. In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X , from independent and identically distributed observations ( X i , Y i ) 1 ≤ i ≤ n . We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This (cid:28)rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε , where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.
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从直接数据或噪声数据对条件密度的非紧致估计
. 本文针对给定X的独立同分布观测值(X i, Y i) 1≤i≤n,提出了Y的条件密度函数的非参数估计策略。我们考虑了一种由非紧支持基生成的l2的投影子空间的回归策略。这(cid:28)第一个研究然后被扩展到没有直接观察到Y,而只有Z = Y + ε的情况,其中ε是已知密度的噪声。在这两种情况下,我们建立和研究了估计量集合,计算了它们在非紧支撑上的各向异性空间上的收敛速率,并证明了相关的下界。然后,我们考虑自适应估计器,我们也证明了风险界限。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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