Assessing the Role of Semi-Parametric Models in Balancing Flexibility and Interpretability in Statistical Estimation

Posted: Aug 21, 2009

• Penelope Parker
• Ryan Long
• Stella Ward

Abstract

The perennial challenge in statistical modeling has been navigating the fundamental tension between model flexibility and interpretability. Parametric models offer the advantage of clear interpretability through well-defined parameters and established inference procedures, but they often impose restrictive assumptions about the underlying data generating process. Conversely, non-parametric approaches provide remarkable flexibility in capturing complex patterns but typically yield models that function as black boxes, offering limited insight into the underlying mechanisms driving the observed phenomena. This research addresses this gap by developing a principled approach to semi-parametric modeling that explicitly optimizes the trade-off between flexibility and interpretability. We introduce the Adaptive Semi-Parametric Estimation with Interpretable Components (ASPEC) framework, which employs a novel regularization scheme to maintain interpretability while accommodating complex data structures. Our work makes three primary contributions: first, we develop a mathematical framework for quantifying the interpretability-flexibility trade-off; second, we propose an adaptive estimation procedure that optimizes this balance; and third, we demonstrate the practical utility of our approach across multiple application domains.