Adaptive Linear Estimating Equations
Adaptive Linear Estimating Equations
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DOI：
10.48550/arxiv.2307.07320
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Mufang Ying;K. Khamaru;Cun-Hui Zhang
中科院分区：
文献类型：
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作者：
Mufang Ying;K. Khamaru;Cun-Hui Zhang
顺序数据收集已成为一种广泛采用的技术，用于提高数据收集过程的效率。尽管有其优点，但这种数据收集机制常常给统计推断过程带来复杂性。例如，自适应线性回归模型中的普通最小二乘 (OLS) 估计器可能会表现出非正态渐近行为，这给准确推理和解释带来了挑战。在本文中，我们提出了一种构建去偏估计器的通用方法来解决这个问题。它利用自适应线性估计方程的思想，建立渐近正态性的理论保证，并辅之以实现接近最优渐近方差的讨论。我们的估计器的一个显着特征是，在多臂老虎机的背景下，我们的估计器保留了最小二乘估计器的非渐近性能，同时获得渐近正态性属性。因此，这项工作有助于连接自适应推理的两个富有成效的范例：a）使用浓度不等式的非渐近推理和b）通过渐近正态性的渐近推理。
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference procedure. For instance, the ordinary least squares (OLS) estimator in an adaptive linear regression model can exhibit non-normal asymptotic behavior, posing challenges for accurate inference and interpretation. In this paper, we propose a general method for constructing debiased estimator which remedies this issue. It makes use of the idea of adaptive linear estimating equations, and we establish theoretical guarantees of asymptotic normality, supplemented by discussions on achieving near-optimal asymptotic variance. A salient feature of our estimator is that in the context of multi-armed bandits, our estimator retains the non-asymptotic performance of the least square estimator while obtaining asymptotic normality property. Consequently, this work helps connect two fruitful paradigms of adaptive inference: a) non-asymptotic inference using concentration inequalities and b) asymptotic inference via asymptotic normality.