Open AccessRobust inference in deconvolution
Author(s) -
Kato Kengo,
Sasaki Yuya,
Ura Takuya
Publication year - 2021
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe1643
Subject(s) - inference , confidence interval , computer science , deconvolution , moment (physics) , completeness (order theory) , confidence and prediction bands , econometrics , latent variable , identity (music) , statistical inference , algorithm , mathematics , statistics , mathematical optimization , artificial intelligence , mathematical analysis , physics , classical mechanics , acoustics
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.