Likelihood inference in the presence of nuisance parameters

TL;DR

This paper reviews recent likelihood-based inference methods involving nuisance parameters, emphasizing plotting likelihood and p-value functions with advanced approximations, and discusses orthogonal parameters and classical inference connections.

Contribution

It introduces recent third order approximation techniques for likelihood and p-value functions, enhancing inference in models with nuisance parameters.

Findings

Improved approximation accuracy for likelihood functions.

Enhanced methods for handling nuisance parameters.

Connections established with classical inference approaches.

Abstract

We describe some recent approaches to likelihood based inference in the presence of nuisance parameters. Our approach is based on plotting the likelihood function and the $p$-value function, using recently developed third order approximations. Orthogonal parameters and adjustments to profile likelihood are also discussed. Connections to classical approaches of conditional and marginal inference are outlined.