Inference on a distribution from noisy draws

Koen Jochmans and Martin Weidner

No CWP44/19, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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. Given a closed-form expression for the bias, bias-corrected estimator of the distribution function and quantile function can be constructed. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. These corrections are non-parametric and easy to implement. 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.

Date: 2019-09-13
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.ifs.org.uk/uploads/CWP4419-Inference-o ... from-noisy-draws.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.ifs.org.uk/uploads/CWP4419-Inference-on-a-distribution-from-noisy-draws.pdf [302 Found]--> https://ifs.org.uk/uploads/CWP4419-Inference-on-a-distribution-from-noisy-draws.pdf)

Related works:
Journal Article: INFERENCE ON A DISTRIBUTION FROM NOISY DRAWS (2024)
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 (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:ifs:cemmap:44/19

Ordering information: This working paper can be ordered from
The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE

Access Statistics for this paper

More papers in CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE. Contact information at EDIRC.
Bibliographic data for series maintained by Emma Hyman ().