We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure to construct asymptotically normal estimators of its linear forms through double‐sample debiasing and low‐rank projection whenever an entry‐wise consistent estimator of the matrix is available. These estimators allow us to subsequently construct confidence intervals for and test hypotheses about the linear forms. Our proposal was motivated by a careful perturbation analysis of the empirical singular spaces under the noisy matrix completion model which might be of independent interest. The practical merits of our proposed inference procedure are demonstrated on both simulated and real‐world data examples.

中文翻译：

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嘈杂矩阵完成的线性形式的统计推断

我们引入了一个灵活的框架，可基于对项的子集的嘈杂观测来推断大矩阵的一般线性形式。特别是，在适度的规则性条件下，只要矩阵的输入一致估计量可用，我们就会开发一种通用程序，通过双样本去偏和低秩投影构造其线性形式的渐近正态估计量。这些估计器使我们能够为线性形式建立可信区间并检验假设。我们的建议是由对有可能具有独立利益的噪声矩阵完成模型下的经验奇异空间的仔细扰动分析所激发的。我们的推理程序的实际优点在模拟和实际数据示例中均得到了证明。