Profile likelihood ratio tests for parameter inferences in generalized single-index models

TL;DR

This paper introduces a profile likelihood ratio test for index coefficients in generalized single-index models, emphasizing its simplicity, invariance, reduced bias, and computational efficiency over existing methods, validated through simulations and real data.

Contribution

It proposes a new profile likelihood ratio test that is easy to implement, bias-reducing, invariant, and significantly faster than existing kernel-based tests.

Findings

Less biased than Wald-tests in finite samples

Over 100 times faster than kernel-based likelihood ratio tests

Effective in simulations and real data analysis

Abstract

A profile likelihood ratio test is proposed for inferences on the index coefficients in generalized single-index models. Key features include its simplicity in implementation, invariance against parametrization, and exhibiting substantially less bias than standard Wald-tests in finite-sample settings. Moreover, the R routine to carry out the profile likelihood ratio test is demonstrated to be over two orders of magnitude faster than the recently proposed generalized likelihood ratio test based on kernel regression. The advantages of the method are demonstrated on various simulations and a data analysis example.