Robust inference in deconvolution

• 成果类型: Article
• 署名作者: Kato, Kengo; Sasaki, Yuya; Ura, Takuya
• 署名单位: Cornell University; Vanderbilt University; University of California System; University of California Davis
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE1643
• 发表日期: 2021
• 页码: 109-142
• 关键词: Deconvolution; measurement error; Robust Inference; uniform confidence band

摘要

Kotlarski's identity has been widely used in applied economic research based on repeated-measurement or panel models with latent variables. However, how to conduct inference for these models has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in repeated measurement error model. The confidence band builds on our finding that we can rewrite Kotlarski's identity as a system of linear moment restrictions. Our approach is robust in that we do not require the completeness. The confidence band controls the asymptotic size uniformly over a class of data generating processes, and it is consistent against all fixed alternatives. Simulation studies support our theoretical results.