Inference on a distribution from noisy draws
Koen Jochmans and
No CWP14/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
We consider a situation where a distribution is being estimated by the empirical distribution of noisy measurements. The measurements errors are allowed to be heteroskedastic and their variance may depend on the realization of the underlying random variable. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias arising from the presence of noise. Conditions are obtained under which this bias is asymptotically non-negligible. Analytical and jackknife corrections for the empirical distribution are derived that recenter the limit distribution and yield con fidence intervals with correct coverage in large samples. Similar adjustments are presented for nonparametric estimators of the density and quantile function. Our approach can be connected to corrections for selection bias and shrinkage estimation. Simulation results confi rm the much improved sampling behavior of the corrected estimators. An empirical application to the estimation of a stochastic-frontier model is also provided.
Keywords: bias correction; nonparametric inference; regression to the mean. (search for similar items in EconPapers)
JEL-codes: C14 C23 (search for similar items in EconPapers)
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Working Paper: Inference on a distribution from noisy draws (2019)
Working Paper: Inference on a Distribution from Noisy Draws (2018)
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