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A general lower bound of minimax risk for absolute‐error loss
Author(s) -
Chen Jeesen
Publication year - 1997
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 - 10.2307/3315347
Subject(s) - minimax , nonparametric statistics , upper and lower bounds , parametric statistics , mathematics , convergence (economics) , estimation , mathematical optimization , statistics , mathematical analysis , economics , management , economic growth
A general lower bound of minimax risk for absolute‐error loss is given in terms of the Hellinger modulus of the estimation problem. The main results are applicable to various parametric, semi‐parametric and nonparametric problems. Two examples of parametric estimation problems and two examples of density estimation problems are given. In all of these examples, the general lower bound achieves the convergence rates of minimax risk.