Inference on a distribution from noisy draws
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 embeddin...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Cambridge University Press
2022
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| Summary: | 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. |
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