{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T02:09:50Z","timestamp":1792462190618,"version":"4.5.0"},"reference-count":60,"publisher":"Institute of Mathematical Statistics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statist. Sci."],"published-print":{"date-parts":[[2019,11,1]]},"abstract":"<jats:p>In the early 1980s, Halbert White inaugurated a \u201cmodel-robust\u201d form of statistical inference based on the \u201csandwich estimator\u201d of standard error. This estimator is known to be \u201cheteroskedasticity-consistent,\u201d but it is less well known to be \u201cnonlinearity-consistent\u201d as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x\\textrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1\/\\sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x\\textrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.<\/jats:p>","DOI":"10.1214\/18-sts693","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T04:00:36Z","timestamp":1578456036000},"page":"523-544","source":"Crossref","is-referenced-by-count":68,"title":["Models as Approximations I: Consequences Illustrated with Linear Regression"],"prefix":"10.1214","volume":"34","author":[{"given":"Andreas","family":"Buja","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lawrence","family":"Brown","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Berk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edward","family":"George","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emil","family":"Pitkin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikhail","family":"Traskin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linda","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"38","doi-asserted-by":"publisher","unstructured":"Liang, K. 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