Date of this Version
The Annals of Statistics
In many nonparametric problems, such as density estimation, nonparametric regression and so on, all the existing informative estimators are biased (asymptotic or finite sample). There has long been a suspicion that either informative unbiased estimators do not exist for such problems or they must be quite complicated. In this paper, we clarify the nonexistence of informative unbiased estimators in all singular problems both for fixed sample size and asymptotically (this includes most problems with optimal rate of convergence slower than n−1/2). We also discuss situations in regular problems where such nonexistences can occur.
unbiasedness, modulus of continuity, Hellinger distance, singular problems
Liu, R. C., & Brown, L. D. (1993). Nonexistence of Informative Unbiased Estimators in Singular Problems. The Annals of Statistics, 21 (1), 1-13. http://dx.doi.org/10.1214/aos/1176349012
Date Posted: 27 November 2017
This document has been peer reviewed.