Quantized Nonparametric Estimation over Sobolev Ellipsoids

25 Mar 2015 Yuancheng Zhu John Lafferty

We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode any estimator, we give tight lower and upper bounds on the excess risk due to quantization in terms of the number of bits, the signal size, and the noise level... (read more)

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