使用估计权重聚合多个估计量

中文摘要 AI 辅助

考虑当仅有估计权重可用时，对数量不断增加的相合估计量进行平均的问题。所关注的潜在参数在各估计量之间可以相同（同质性）或不同（异质性）。本文的贡献有三方面。第一，证明了估计权重与估计量的交互作用可能产生特定的偏误项。这限制了在推断中忽略权重估计时能够聚合的估计量数量。第二，本文提出了估计的自适应权重，该权重能够以统一的方式实现标准高斯推断，并在同质性和异质性下均具有渐近最优性。第三，给出了确保Cochran（1937）提出的基于估计方差的同质性Q检验有效性的条件。

英文摘要

Consider an increasing number of consistent estimators to be averaged when only estimated weights are available. The underlying parameter of interest can be identical across estimators (homogeneity) or not (heterogeneity). The contribution of the paper is threefold. First, it is shown that the interaction of the estimated weights with the estimators can generate specific bias terms. This constrains the number of estimators that can be aggregated when weight estimation is ignored in inference. Second, the paper proposes estimated adaptive weights, which allow for standard Gaussian inference in a uniform manner and are asymptotically optimal both under homogeneity and heterogeneity. Third, conditions ensuring the validity of the Cochran (1937) Q test of homogeneity with estimated variance are given.

发表机构

• Queen Mary, University of London（伦敦大学玛丽女王学院）
• CNRS, INRAE, Institut Agro Dijon & Université Grenoble Alpes（法国国家科学研究中心、法国国家农业食品与环境研究院、第戎高等农学院与格勒诺布尔阿尔卑斯大学）

机构由 AI 辅助整理，请以论文原文为准。