论文标题
在稀疏相检索中为信号构建置信区间
Constructing Confidence Intervals for the Signals in Sparse Phase Retrieval
论文作者
论文摘要
在本文中，我们提供了一种一般方法，以在稀疏期检索中对它们的单个信号坐标或线性组合进行统计推断。给定针对目标参数的初始估计器（信号的某些简单函数），该估计是由某些现有算法生成的，我们可以以修改版本的渐近正常且无偏见的方式对其进行修改。然后，可以根据这种渐近正态性构建置信区间和假设检验。为了简明性，我们专注于这项工作的置信区间，而假设检验可以采用类似的程序。在一些对信号和样本量的轻度假设下，我们为提出的方法建立了理论保证。这些假设通常是较弱的，因为尺寸可以超过样本量，并且允许许多非零的小坐标。此外，理论分析表明，单个坐标的修改估计器具有统一的界限，因此可以同时进行间隔估计。在广泛的设置中的数值模拟支持我们的理论结果。
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple function of the signal), which is generated by some existing algorithm, we can modify it in a way that the modified version is asymptotically normal and unbiased. Then confidence intervals and hypothesis testings can be constructed based on this asymptotic normality. For conciseness, we focus on confidence intervals in this work, while a similar procedure can be adopted for hypothesis testings. Under some mild assumptions on the signal and sample size, we establish theoretical guarantees for the proposed method. These assumptions are generally weak in the sense that the dimension could exceed the sample size and many non-zero small coordinates are allowed. Furthermore, theoretical analysis reveals that the modified estimators for individual coordinates have uniformly bounded variance, and hence simultaneous interval estimation is possible. Numerical simulations in a wide range of settings are supportive of our theoretical results.
