This paper studies the estimation of the conditional density f (x, $\times$) of Y i given X i = x, from the observation of an i.i.d. sample (X i , Y i) $\in$ 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).

翻译：本文研究Y i 给X i = x 的有条件密度 f (x, $\ times $) 的估算,从对 i.d 样本( X i, Y i) 的观察( X i, Y i) $\ in $ R d, i = 1.., n 。 我们假设f 只取决于 r 未知的成分, 通常 r d., n 。 我们根据内核规则提供适应性的全非对称战略,以估计 f. 为了选择我们内核规则的带宽,我们提议了一个新的快速迭代算法,由Rodeo 算法( Wasserman 和 Lafferty (2006)) 启发,以探测 f. 更精确地说,在迷你Max 设置中,我们精准的估测算器,既适应常规性,又适应紧张性的, 也达到准最佳的趋同率。 我们的计算复杂度只有 O( dn log n) 。