设计矩阵正交时基于SLOPE的模式恢复和信号去噪
Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal
摘要：
排序$\ell_1$惩罚估计（SLOPE）是一种用于拟合高维回归模型的相对较新的凸正则化方法。SLOPE允许通过将回归系数的某些估计值完全缩小为零或通过使这些系数的某些非零估计值的绝对值相等来降低模型维数。这允许识别其中一些~真回归系数相等的情况。在本文中，我们将介绍SLOPE模式，即，真实回归系数之间的关系集，可以通过SLOPE来识别。我们还将提出新的结果的强一致性的SLOPE估计和~的~强一致性的模式恢复的~SLOPE时，设计矩阵是正交的，并说明优势的~的~SLOPE聚类的背景下，高频信号去噪。
英文摘要：
Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression coefficients completely to zero or by equating the absolute values of some nonzero estimates of these coefficients. This allows to identify situations where some of~true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on~the~strong consistency of pattern recovery by~SLOPE when the design matrix is orthogonal and illustrate advantages of~the~SLOPE clustering in the context of high frequency signal denoising.
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