A kernel density estimator is defined to be admissible if no other kernel estimator has (among all densities and sample sizes) uniformly smaller mean integrated squared error. Admissible kernel density estimators are precisely those using kernels with nonnegative Fourier transforms bounded by 1. Several examples are given.
"Admissibile Kernel Estimators of a Multivariate Density." Ann. Statist. 16 (4) 1421 - 1427, December, 1988. https://doi.org/10.1214/aos/1176351046