论文标题
稀疏多元功能主成分分析的准参数率
Quasi-parametric rates for Sparse Multivariate Functional Principal Components Analysis
论文作者
论文摘要
这项工作旨在给出非反应结果，以估算多元随机过程的第一个主要成分。我们首先在多元案例中定义协方差函数和协方差操作员。然后，我们定义一个投影操作员。该操作员可以看作是功能数据分析上下文中原始数据的重建步骤。接下来，我们表明特征元素可以表示为优化问题的解决方案，并介绍了此优化问题的套索变体和相关的插件估计器。最后，我们评估估计器的准确性。我们在特征元的均方根重建误差上建立了一个minimax下限，这证明该过程在最小值中具有最佳的差异。
This work aims to give non-asymptotic results for estimating the first principal component of a multivariate random process. We first define the covariance function and the covariance operator in the multivariate case. We then define a projection operator. This operator can be seen as a reconstruction step from the raw data in the functional data analysis context. Next, we show that the eigenelements can be expressed as the solution to an optimization problem, and we introduce the LASSO variant of this optimization problem and the associated plugin estimator. Finally, we assess the estimator's accuracy. We establish a minimax lower bound on the mean square reconstruction error of the eigenelement, which proves that the procedure has an optimal variance in the minimax sense.
