This paper presents the nonparametric inference problem about the probability density function of a latent variable in the measurement error model with repeated measurements. We construct a system of linear complex-valued moment restrictions by Kotlarski's identity , and then establish a confidence band for the density of the latent variable. Our 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.
Kotlarski's identity has been widely used in applied economic research. However, how to conduct inference based on this popular identification approach 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. 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.
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This paper presents the nonparametric inference problem about the probability
Kotlarski's identity has been widely used in applied economic research. However, how to conduct inference based on this popular identification approach has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the
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with repeated measurements. We construct a system of linear complex-valued moment restrictions by
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