Bilinear Form Test: Theoretical Properties and Applications

Abstract

The present thesis investigates the Bilinear Form Test (BF Test) as a robust statistical tool for evaluating parameter constraints across various models. It examines the test's theoretical foundations, with a particular focus on its invariance under reparameterizations and its performance in finite-sample settings. By leveraging bilinear forms, the BF Test provides an alternative to likelihood-based methods, employing an asymptotic chi-squared distribution that simplifies hypothesis testing. Monte Carlo simulations and empirical applications—including its use in financial models like the Capital Asset Pricing Model (CAPM) and in Generalized Estimating Equations (GEE) for correlated data—demonstrate the method’s efficiency, robustness, and versatility. Key contributions of this work include a detailed exploration of the BF Test's theoretical properties, validation of its invariance across different model structures, and a comprehensive comparison with traditional testing approaches, alongside proposed extensions for future research.