标题： 弱相依过程边际密度的逐点自适应估计 显示英文标题

标题： Pointwise Adaptive Estimation of the MarginalDensity of a Weakly Dependent Process

摘要： 本文致力于弱相依过程公共边际密度函数的估计。 估计的准确性通过点态风险来衡量。 我们提出了一个基于核规则的数据驱动程序。 带宽选择采用Goldenshluger和Lepski的方法，并证明所得估计量满足一种oracle型不等式。 该方法也被证明是自适应的（在minimax框架下）针对多种类型的依赖性下的Hölder球：可以考虑强混合过程、$\lambda$-相依过程或独立同分布序列，使用单一的估计程序即可。 一些模拟实验展示了所提出方法的性能。 显示英文摘要

摘要： This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth is selected using the approach of Goldenshluger and Lepski and we prove that the resulting estimator satisfies an oracle type inequality. The procedure is also proved to be adaptive (in a minimax framework) over a scale of H\"older balls for several types of dependence: stong mixing processes, $\lambda$-dependent processes or i.i.d. sequences can be considered using a single procedure of estimation. Some simulations illustrate the performance of the proposed method.