{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/89048"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/89048","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"MMSE estimation from quantized observations in the nonasymptotic regime","abstract":"This thesis studies MMSE estimation on the basis of quantized noisy observations. It presents nonasymptotic bounds on MMSE regret due to quantization for two settings: (1) estimation of a scalar random variable given a quantized vector of n conditionally independent observations, and (2) estimation of a p-dimensional random vector given a quantized vector of n observations (not necessarily independent) when the full MMSE estimator has a sub-Gaussian concentration property.","abstract_html":"This thesis studies MMSE estimation on the basis of quantized noisy observations. 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