Testing Goodness-of-Fit for Conditional Distributions: A New Perspective based on Principal Component Analysis

Abstract: This paper introduces a novel goodness-of-fit test technique for parametric conditional distributions. The proposed tests are based on a residual marked empirical process, for which we develop a conditional Principal Component Analysis. The obtained components provide a basis for various types of new tests in addition to the omnibus one. Component tests that based on each component serve as experts in detecting certain directions. Smooth tests that assemble a few components are also of great use in practice. To further improve testing performance, we introduce a component selection approach, aiming to identify the most contributory components. The finite sample performance of the proposed tests is illustrated through Monte Carlo experiments.