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 |
|---|---|
| Journal | Journal of Econometrics |
| DOIs | |
| Publication status | Accepted/In press - 2019 Jan 1 |
| Externally published | Yes |
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Keywords
- Confidence band
- Deconvolution
- Measurement error
- Stochastic dominance
ASJC Scopus subject areas
- Economics and Econometrics
Cite this
Inference on distribution functions under measurement error. / Adusumilli, Karun; Kurisu, Daisuke; Otsu, Taisuke; Whang, Yoon Jae.
In: Journal of Econometrics, 01.01.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Inference on distribution functions under measurement error
AU - Adusumilli, Karun
AU - Kurisu, Daisuke
AU - Otsu, Taisuke
AU - Whang, Yoon Jae
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Confidence band
KW - Deconvolution
KW - Measurement error
KW - Stochastic dominance
UR - http://www.scopus.com/inward/record.url?scp=85072610740&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072610740&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2019.09.002
DO - 10.1016/j.jeconom.2019.09.002
M3 - Article
AN - SCOPUS:85072610740
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
ER -