On the Statistical Complexity of Sample Amplification. (arXiv:2201.04315v1 [math.ST])

Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it
possible to produce a larger set of $n+m$ samples which cannot be distinguished
from $n+m$ i.i.d. samples drawn from $P$? (Axelrod et al. 2019) formalized this
question as the sample amplification problem, and gave optimal amplification
procedures for discrete distributions and Gaussian location models. However,
these procedures and associated lower bounds are tailored to the specific
distribution classes, and a general statistical understanding of sample
amplification is …

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