论文标题
在实际线上非参数密度估计中数据驱动的聚合
Data-driven aggregation in non-parametric density estimation on the real line
论文作者
论文摘要
我们研究了未知密度的非参数估计，并在R（分别为R+）中支持。提出的估计过程基于对Hermite（分别是Laguerre）函数跨越有限维数的投影。本文的重点是引入数据驱动的聚合方法，以应对即将到来的偏见差异。我们的新过程将通常的模型选择方法作为极限情况集成。我们显示了数据驱动的聚合密度估计器的Oracle-和最小值 - 因此其适应性。我们提出了一项模拟研究的结果，该研究可以使用模型选择与新聚合相比，可以比较数据驱动的估计器的有限样本性能。
We study non-parametric estimation of an unknown density with support in R (respectively R+). The proposed estimation procedure is based on the projection on finite dimensional subspaces spanned by the Hermite (respectively the Laguerre) functions. The focus of this paper is to introduce a data-driven aggregation approach in order to deal with the upcoming bias-variance trade-off. Our novel procedure integrates the usual model selection method as a limit case. We show the oracle- and the minimax-optimality of the data-driven aggregated density estimator and hence its adaptivity. We present results of a simulation study which allow to compare the finite sample performance of the data-driven estimators using model selection compared to the new aggregation.
