Accurate Parametric Inference for Small Samples

TL;DR

This paper demonstrates practical implementation of modern likelihood theory for small sample inference across various models, emphasizing numerical methods and applications over theoretical asymptotics.

Contribution

It introduces a sampling approach for nonlinear models and advocates for likelihood approximations over exact procedures in logistic regression.

Findings

Likelihood methods can be effectively applied in small samples.

Sampling approaches improve inference in nonlinear models.

Likelihood approximations often outperform exact methods in logistic regression.

Abstract

We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical asymptotic approximations, the focus of this paper is not on theory but on implementation and applications. Numerical illustrations are given for logistic regression, nonlinear models, and linear non-normal models, and we describe a sampling approach for the third of these classes. In the case of logistic regression, we argue that approximations are often more appropriate than `exact' procedures, even when these exist.