Resampled Statistics for Dependence-Robust Inference
📝 Original Paper Info
- Title: Dependence-Robust Inference Using Resampled Statistics- ArXiv ID: 2002.02097
- Date: 2021-08-26
- Authors: Michael P. Leung
📝 Abstract
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that the statistics are asymptotically normal under the weak requirement that the target parameter can be consistently estimated at the parametric rate. This holds for regular estimators under many well-known forms of weak dependence and justifies the claim of dependence-robustness. We consider applications to settings with unknown or complicated forms of dependence, with various forms of network dependence as leading examples. We develop tests for both moment equalities and inequalities.💡 Summary & Analysis
This research paper focuses on developing robust inference procedures that account for general forms of weak dependence in data. The primary issue addressed is the impact of unknown or complex dependencies within datasets, which can undermine traditional statistical testing methods. To solve this, the authors utilize resampling techniques to construct test statistics independent of the underlying correlation structure.The core technique involves a systematic approach to generate new samples from the original dataset through resampling, ensuring that these newly constructed statistics converge to a normal distribution asymptotically under certain consistency conditions. The research proves that if the target parameter can be estimated consistently at a parametric rate, then the test statistics will follow an asymptotic normal distribution, thus providing robustness against various forms of weak dependence.
The significance of this work lies in its ability to handle complex and unknown dependencies within data, making it particularly useful for fields like network analysis where such dependencies are common. The development of tests for moment equalities and inequalities further enhances its practical applicability.