论文标题
正规化桥式估计有多次罚款
Regularized Bridge-type estimation with multiple penalties
论文作者
论文摘要
本文的目的是引入一个自适应惩罚估计量，以识别稀疏性假设下的真正减少参数模型。特别是，我们处理了一个框架，在该框架中，未确定的结构参数估计值同时需要多个收敛速率（即所谓的混合率渐近行为）。我们通过考虑涉及$ \ ell^q $ narms $（0 <q \ leq 1）$的罚款功能来引入桥梁型估计器。我们证明所提出的正则化估计器满足了Oracle属性。 我们的方法对于参数稀疏设置中随机微分方程的估计很有用。更确切地说，在高频观察方案下，我们将方法应用于沿阵行的扩散，并引入了选择调谐参数的程序。此外，本文包含了一项模拟研究以及真实的数据预测，以评估所提出的桥梁估计器的性能。
The aim of this paper is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity assumption. In particular, we deal with the framework where the unpenalized estimator of the structural parameters needs simultaneously multiple rates of convergence (i.e. the so-called mixed-rates asymptotic behavior). We introduce a Bridge-type estimator by taking into account penalty functions involving $\ell^q$ norms $(0<q\leq 1)$. We prove that the proposed regularized estimator satisfies the oracle properties. Our approach is useful for the estimation of stochastic differential equations in the parametric sparse setting. More precisely, under the high frequency observation scheme, we apply our methodology to an ergodic diffusion and introduce a procedure for the selection of the tuning parameters. Furthermore, the paper contains a simulation study as well as a real data prediction in order to assess about the performance of the proposed Bridge estimator.
