INFERENCE ON A DISTRIBUTION FROM NOISY DRAWS

Koen Jochmans and Martin Weidner

Econometric Theory, 2024, vol. 40, issue 1, 60-97

Abstract: We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators. An empirical illustration on heterogeneity in deviations from the law of one price is equally provided.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
Working Paper: Inference on a distribution from noisy draws (2022)
Working Paper: Inference on a Distribution from Noisy Draws (2021)
Working Paper: Inference on a distribution from noisy draws (2021)
Working Paper: Inference On A Distribution From Noisy Draws (2021)
Working Paper: Inference on a distribution from noisy draws (2019)
Working Paper: Inference on a distribution from noisy draws (2019)
Working Paper: Inference on a distribution from noisy draws (2018)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:40:y:2024:i:1:p:60-97_3

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().