Can Distributed Uniformity Testing Be Local?. Meir, U., Minzer, D., & Oshman, R. In 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, pages 228–237, 2019. ACM.
[MMO19] Considers a similar setting as [FMO18], but allowing $\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\ell$-bit Boolean function.

bibtex   
@inproceedings{MMO19,
  author    = {Uri Meir and
               Dor Minzer and
               Rotem Oshman},
  title     = {Can Distributed Uniformity Testing Be Local?},
  booktitle = {2019 {ACM} Symposium on Principles of Distributed Computing, {PODC} 2019},
  pages     = {228--237},
  publisher = {{ACM}},
  year      = {2019},
  bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[MMO19]</span> Considers a similar setting as [FMO18], but allowing $\ell$ bits per user, and also arbitrary aggregation rules (i.e., in this case, the same public-coin SMP setting as in [ACT20b], but allowing for several samples per users and trying to minimize this number). The proofs rely on Boolean Fourier analysis, seeing the decision rule as an $n\ell$-bit Boolean function.</div>}
}

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