2026-09-20T07:22:55Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/90776 2023-07-11 col_2142_5131 com_2142_5130

Wu, Yihong Yang, Pengkun 2016-07-07T20:27:34Z 2016-07-07T20:27:34Z 2018-07-08T09:15:36Z 2016-04-19 2016-05 Consider the problem of estimating the Shannon entropy of a distribution over k elements from n independent samples. We obtain the minimax mean- square error within universal multiplicative constant factors if n exceeds a constant factor of k/log(k); otherwise there exists no consistent estimator. This refines the recent result of Valiant and Valiant (2011) that the mini- mal sample size for consistent entropy estimation scales. The apparatus of best polynomial approximation plays a key role in both the construction of optimal estimators and, via a duality argument, the minimax lower bound. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01 The student, Pengkun Yang, accepted the attached license on 2016-04-18 at 09:01. The student, Pengkun Yang, submitted this Thesis for approval on 2016-04-18 at 09:10. This Thesis was approved for publication on 2016-04-19 at 11:16. DSpace SAF Submission Ingestion Package generated from Vireo submission #9287 on 2016-07-07 at 13:49:50 Made available in DSpace on 2016-07-07T20:27:34Z (GMT). No. of bitstreams: 2 YANG-THESIS-2016.pdf: 437966 bytes, checksum: 56a247801d3c1d9b592a498347b02e4b (MD5) LICENSE.txt: 4209 bytes, checksum: 45523ffcb7e2b421561eb00e4bfccfa7 (MD5) Previous issue date: 2016-04-19 Embargo set by: Seth Robbins for item 93128 Lift date: 2018-07-07T20:28:14Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 93128 Lift date: 2018-07-07T20:35:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 93128 on 2018-07-08T09:15:36Z. application/pdf http://hdl.handle.net/2142/90776 en Copyright 2016 Pengkun Yang entropy estimation large alphabet Optimal entropy estimation on large alphabet: fundamental limits and fast algorithms text text Electrical & Computer Eng Electrical & Computer Engr University of Illinois at Urbana-Champaign Thesis M.S.