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Consistent maximum likelihood estimation of a unimodal density using shape restrictions
Author(s) -
Meyer Mary C.,
Woodroofe Michael
Publication year - 2004
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316001
Subject(s) - estimator , hellinger distance , almost everywhere , maximum likelihood , interval (graph theory) , mathematics , convergence (economics) , mode (computer interface) , metric (unit) , rate of convergence , maximum likelihood sequence estimation , statistics , mathematical optimization , computer science , combinatorics , mathematical analysis , engineering , computer network , channel (broadcasting) , operations management , economics , economic growth , operating system
It is well known that the unimodal maximum likelihood estimator of a density is consistent everywhere but at the mode. The authors review various ways to solve this problem and propose a new estimator that is concave over an interval containing the mode; this interval may be chosen by the user or through an algorithm. The authors show how to implement their solution and compare it to other approaches through simulations. They show that the new estimator is consistent everywhere and determine its rate of convergence in the Hellinger metric.