二次度量回归模型中折叠凹惩罚估计的统计性质
Folded Concave Penalized Estimation for Quadratic Measurements Regression
摘要: 目前，关于二次度量回归模型的研究受到了广泛关注，比如相位恢复、动力系统状态估计、无标记的距离几何和各种组合图等问题。本文考虑从高维二次度量回归模型中恢复未知信号。通过采用折叠凹惩罚最小二乘估计方法，我们得到了真实信号与估计值之间的误差界。并且结果中还表明估计值与真实值有相同的支撑集。另外，文章中我们主要研究SACD和MCP两种典型的折叠凹惩罚函数。
Abstract: Recovering an unknown signal from quadratic measurements has gained more attention, such as phase retrieval, power system state estimation and the unlabeled distance geometry problem. In this paper, we reconstruct the unknown signal from high-dimensional quadratic measurements. By employing folded concave penalized least squares method, our main result shows the non- asymp-totic error bound between the estimator and the true signal. Our result shows that the estimator has the same support set as the true signal. In addition, we focus on two typical folding concave penalty functions, SCAD and MCP.
文章引用：张馨玉, 杨婧昱. 二次度量回归模型中折叠凹惩罚估计的统计性质[J]. 应用数学进展, 2023, 12(10): 4357-4364. https://doi.org/10.12677/AAM.2023.1210429

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