## Self‐concordance for empirical likelihood

### Abstract

#### Abstract

The usual approach to computing empirical likelihood for the mean uses Newton's method after eliminating a Lagrange multiplier and replacing the function $-\text{log}\left(x\right)$ 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

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