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 inducement of replication under the postulated model. This can be cast in terms of some non-standard inferential separations, in the vein of Fisherian ancillarity/co-ancillarity and sufficiency/co-sufficiency separations, allowing the replacement of 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.

翻译：我们基于参数统计推断的基本原理视角，研究半参数模型及其他高参数化模型的评估方法。在此过程中，我们揭示了避免常规半参数方法（通常需要通过核平滑或基扩展估计冗余分量，且伴随调节参数选择困难，导致估计与模型评估界限模糊）的可能性。核心在于通过假设模型诱导复制机制，这可通过非标准推断分离（类似于Fisher辅助性/共辅助性、充分性/共充分性分离）实现，从而用某类样本内预测误差替代样本外预测误差作为半参数模型评估准则。基于此框架，我们在多个实例场景中提出了新方法论贡献，包括：比例风险模型、具有半参数强度函数的时变泊松过程、配对样本及两样本案例的模型评估。该框架还涵盖稀疏回归模型置信集构建的后约简推断方法。数值实验证实，该方法在假设模型下能恢复名义误差率，并对半参数替代方向的偏离具有高敏感性。最后，我们强调待解决的开放性挑战并给出统一性展望。