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