The minimax L2 rate for distributed nonparametric estimation is (Ness)^(-2r/(2r+1)) up to logarithmic factors, where Ness is a single phase-transition formula of m, n, l, and r.
Adaptive distributed method s under communication constraints,
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Distributed Nonparametric Estimation: from Sparse to Dense Samples per Terminal
The minimax L2 rate for distributed nonparametric estimation is (Ness)^(-2r/(2r+1)) up to logarithmic factors, where Ness is a single phase-transition formula of m, n, l, and r.