标题： 单指标模型中使用聚合的最优速率和适应性 显示英文标题

标题： Optimal rates and adaptation in the single-index model using aggregation

摘要： 我们希望恢复单指标模型中的回归函数。使用带有局部多项式估计器的聚合算法，我们特别回答了 Stone（1982）提出的第 2 个问题，即关于此模型内的最优收敛速度。这里构造的过程具有很强的适应性：它既适应链接函数的光滑度，又适应未知指标。此外，该过程局部适应数据分布，从而可以证明对于相当一般的实验设计的结果。通过数值模拟研究了该算法的行为。特别是，我们通过实证表明，它显著改善了经验风险最小化。 显示英文摘要

摘要： We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to Question 2 from Stone (1982) on the optimal convergence rate within this model. The procedure constructed here has strong adaptation properties: it adapts both to the smoothness of the link function and to the unknown index. Moreover, the procedure locally adapts to the distribution of the data, which allows to prove the results for a fairly general design. The behavior of this algorithm is studied through numerical simulations. In particular, we show empirically that it improves strongly empirical risk minimization.