Abstract
This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X=X∗+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗ . We allow the density of ϵ to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ϵ is known. Our approximation results are applicable to various contexts, such as confidence bands for FX∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X∗, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.
Original language | English |
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Pages (from-to) | 131-164 |
Number of pages | 34 |
Journal | Journal of Econometrics |
Volume | 215 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2020 Mar |
Externally published | Yes |
Keywords
- Confidence band
- Deconvolution
- Measurement error
- Stochastic dominance
ASJC Scopus subject areas
- Economics and Econometrics