Premium
Self‐concordance for empirical likelihood
Author(s) -
Owen Art B.
Publication year - 2013
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 - 10.1002/cjs.11183
Subject(s) - quartic function , lagrange multiplier , quadratic equation , mathematics , convergence (economics) , function (biology) , steffensen's method , backtracking , quadratic function , statistics , mathematical optimization , local convergence , newton's method in optimization , iterative method , pure mathematics , economics , geometry , evolutionary biology , biology , economic growth
Abstract The usual approach to computing empirical likelihood for the mean uses Newton's method after eliminating a Lagrange multiplier and replacing the function − log ( x ) by a quadratic Taylor approximation to the left of 1 / n . This paper replaces the quadratic approximation by a quartic. The result is a self‐concordant function for which Newton's method with backtracking has theoretical convergence guarantees. The Canadian Journal of Statistics 41: 387–397; 2013 © 2013 Statistical Society of Canada
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom