Models as Approximations I: Consequences Illustrated with Linear Regression

• Andreas Buja ; Lawrence Brown ; Richard Berk ^[1] ; Edward George ^[1] ; Emil Pitkin ^[1] ; Mikhail Traskin ^[1] ; Kai Zhang ; Linda Zhao
  1. [1] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
• Localización: Statistical science, ISSN 0883-4237, Vol. 34, Nº. 4, 2019 (Ejemplar dedicado a: Memorial Issue for Lawrence D. Brown), págs. 523-544
• Idioma: inglés
• DOI: 10.1214/18-sts693
• Texto completo no disponible (Saber más ...)
• Resumen

  • In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” 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-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/ √ N; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the x-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.