🤖 AI Summary
This paper addresses the goodness-of-fit testing problem for parametric conditional distribution models. We propose a novel method based on residual-marked empirical processes and Conditional Principal Component Analysis (CPCA). Our key contributions are threefold: (i) we introduce CPCA into the distributional testing framework for the first time, constructing three types of test statistics—global, single-directional, and smoothed-combination; (ii) we design an adaptive component selection mechanism that automatically identifies the most discriminative principal components, thereby enhancing directional sensitivity and statistical power; and (iii) Monte Carlo experiments demonstrate that the proposed method significantly outperforms classical tests (e.g., Kolmogorov–Smirnov and Cramér–von Mises types) in finite samples, especially under strong heterogeneity or tail deviations. The approach provides a flexible, interpretable, and powerful framework for conditional distribution validation.
📝 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 efficiency, 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.