Paper gives exact global minimax risk near nonidentification
Conditions let one estimator match the leading constant uniformly; two models fix fifth- and sixth-order risk constants.
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Relatederrors-in-variables1minimax1nonidentification1score-matching1stein-operators1unnormalized-models1
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Paper links scoring rules and Stein operators for unnormalized models
The framework covers score matching, ratio matching, pseudolikelihood and noise contrastive estimation, then characterizes estimator efficiency.