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.

中文翻译：

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反卷积的可靠推断

Kotlarski的身份已被广泛用于基于重复测量或具有潜在变量的面板模型的应用经济研究中。但是，如何对这些模型进行推理已经有二十年了。本文通过为重复测量误差模型中的潜在变量的密度函数构造一个新的置信带来解决这个开放问题。置信带基于我们的发现，即我们可以将Kotlarski的身份重写为线性力矩限制系统。我们的方法很健壮，因为我们不需要完整性。置信带在一类数据生成过程中均匀地控制渐近大小，并且与所有固定替代方法一致。仿真研究支持我们的理论结果。