Arbeitspapier

Inference on a distribution from noisy draws

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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.

Language: Englisch

Bibliographic citation: Series: cemmap working paper ; No. CWP42/21

Classification: Wirtschaft
Semiparametric and Nonparametric Methods: General
Single Equation Models; Single Variables: Panel Data Models; Spatio-temporal Models

Subject: bias correction
estimation noise
nonparametric inference
measurement error
panel data
regression to the mean
shrinkage

Event: Geistige Schöpfung

(who): Jochmans, Koen
Weidner, Martin

Event: Veröffentlichung

(who): Centre for Microdata Methods and Practice (cemmap)

(where): London

(when): 2021

DOI: doi:10.47004/wp.cem.2021.4221

Handle: http://hdl.handle.net/10419/260378

Last update: 10.03.2025, 11:44 AM CET

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Object type

Arbeitspapier

Associated

Jochmans, Koen
Weidner, Martin
Centre for Microdata Methods and Practice (cemmap)

Time of origin

2021

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