Buja, Andreas; Kuchibhotla, Arun Kumar; Berk, Richard; George, Edward; Tchetgen Tchetgen, Eric; Zhao, Linda Rejoinder: Models as approximations. (English) Zbl 1440.62022 Stat. Sci. 34, No. 4, 606-620 (2019). Summary: We respond to the discussants of our articles emphasizing the importance of inference under misspecification in the context of the reproducibility/replicability crisis. Along the way, we discuss the roles of diagnostics and model building in regression as well as connections between our well-specification framework and semiparametric theory.Reply to the comments [Zbl 1440.62026; Zbl 1440.62024; Zbl 1440.62029; Zbl 1440.62027; Zbl 1440.62023; Zbl 1440.62031; Zbl 1440.62028; Zbl 1440.62025] to the authors’ papers [ibid. 34, No. 4, 523–544 (2019; Zbl 1440.62020); ibid. 34, No. 4, 545–565 (2019; Zbl 1440.62021)]. MSC: 62A01 Foundations and philosophical topics in statistics 62J05 Linear regression; mixed models 62J20 Diagnostics, and linear inference and regression 62D20 Causal inference from observational studies Keywords:well-specification; reproducibility/replicability; proper scoring rules; causal inference; semiparametrics; diagnostics Citations:Zbl 1440.62026; Zbl 1440.62024; Zbl 1440.62029; Zbl 1440.62027; Zbl 1440.62023; Zbl 1440.62031; Zbl 1440.62028; Zbl 1440.62025; Zbl 1440.62020; Zbl 1440.62021 Software:GeneralisedCovarianceMeasure; conformalInference × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Adam, D. (2019). Psychology’s reproducibility solution fails first test. Science 364 813. 10.1126/science.364.6443.813. [2] Aronov, P. M. and Miller, B. T. (2019). Foundations of Agnostic Statistics. Cambridge Univ. Press, Cambridge. [3] Athey, S. and Imbens, G. (2017). The econometrics of randomized experiments. 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