Necessary and sufficient conditions for zero-rate density estimation

This work addresses the problem of universal density estimation under an operational data-rate constraint. We present a coding theorem that stipulates necessary and sufficient conditions to learn and transmit a memoryless source distribution with arbitrary precision (in total variations), under an asymptotic zero-rate regime, in bits per sample. In the process, we propose a concrete coding scheme to achieve this learning objective, adopting the Skeleton estimate developed by Y. Yatracos [1], [2].