Specification testing for regressions: an approach bridging between local smoothing and global smoothing methods

TL;DR

This paper introduces a projection-based regression specification test that combines local and global smoothing advantages, improving detection of various alternatives with a kernel estimation approach.

Contribution

A novel projection-based test that bridges local and global smoothing methods, enhancing sensitivity and robustness in regression specification testing.

Findings

The test has favorable asymptotic properties.

Simulation studies show improved finite sample performance.

Real data analysis confirms practical effectiveness.

Abstract

For regression models, most of existing specification tests can be categorized into the class of local smoothing tests and of global smoothing tests. Compared with global smoothing tests, local smoothing tests can only detect local alternatives distinct from the null hypothesis at a much slower rate when the dimension of predictor vector is high, but can be more sensitive to oscillating alternatives. In this paper, we suggest a projection-based test to bridge between the local and global smoothing-based methodologies such that the test can benefit from the advantages of these two types of tests. The test construction is based on a kernel estimation-based method and the resulting test becomes a distance-based test with a closed form. The asymptotic properties are investigated. Simulations and a real data analysis are conducted to evaluate the performance of the test in finite sample cases.