Induced replication and the assessment of models

2026-03-29

AI Summary

This study addresses the challenges of tuning and evaluation ambiguity in semiparametric and high-dimensional models arising from redundant components introduced by kernel smoothing or basis expansions. The authors propose an induced replication framework that leverages the principle of parametric inference, transforming model assessment into an in-sample prediction error problem by exploiting known replication mechanisms embedded within the model. Building upon Fisher’s concepts of sufficiency and conditional sufficiency, this approach replaces conventional out-of-sample prediction and is applicable to proportional hazards models, time-varying Poisson processes, and confidence set construction for sparse regression. Both theoretical analysis and numerical experiments demonstrate that the method accurately controls nominal error rates under correct model specification and exhibits high sensitivity to semiparametric misspecification.

Abstract

We study the assessment of semiparametric and other highly-parametrised models from the perspective of foundational principles of parametric statistical inference. In doing so, we highlight the possibility of avoiding the usual semiparametric considerations, which typically require estimation of nuisance components through kernel smoothing or basis expansion, with the associated difficulties of tuning-parameter choice that blur the distinction between estimation and model assessment. A key aspect is the availability of preliminary manoeuvres that induce an internal replication of known form under the postulated model. This can be cast as a generalised version of the Fisherian sufficiency/co-sufficiency separation, replacing out-of-sample prediction error as a criterion for semiparametric model assessment by a type of within-sample prediction error. Framed in this light are new methodological contributions in multiple example settings, including model assessment for the proportional hazards model, for a time-dependent Poisson process with semiparametric intensity function, and for matched-pair and two-group examples. Also subsumed within the framework is a post-reduction inference approach to the construction of confidence sets of sparse regression models. Numerical work confirms recovery of nominal error rates under the postulated model and high sensitivity to departures in the direction of semiparametric alternatives. We conclude by emphasising open challenges and unifying perspectives.

Problem

• model assessment
• semiparametric models
• induced replication
• nuisance parameters
• within-sample prediction

Innovation

• induced replication
• semiparametric model assessment
• within-sample prediction error
• co-sufficiency
• post-reduction inference