Composite Likelihood Inference by Nonparametric Saddlepoint Tests

TL;DR

This paper introduces a nonparametric saddlepoint test for composite likelihood inference that improves hypothesis testing accuracy without relying on the Godambe information matrix, demonstrated through simulations.

Contribution

It develops a new saddlepoint test statistic for composite likelihood inference that is asymptotically chi-square and independent of the Godambe information matrix.

Findings

The proposed test achieves second-order accuracy.

Simulation studies confirm improved inference accuracy.

The method is robust to misspecification of the Godambe information.

Abstract

The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strenght of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently inaccurate estimates of the Godambe information translate in inaccurate p-values. In this paper it is shown how accurate inference can be obtained by using a fully nonparametric saddlepoint test statistic derived from the composite score functions. The proposed statistic is asymptotically chi-square distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies.