INFERENCE ON A DISTRIBUTION FROM NOISY DRAWS

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