Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?
Volume 22 / 1993
Applicationes Mathematicae 22 (1993), 103-115
DOI: 10.4064/am-22-1-103-115
Abstract
The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.
