2014/04/06 by Andreas Buja, Buja, Andreas, Richard A. Berk +13
Mathematics · #Advanced Statistical Methods and Models #Statistical Methods and Inference #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1404.1578
In the early 1980s Halbert White inaugurated a "model-robust'' form of\nstatistical inference based on the "sandwich estimator'' of standard error.\nThis estimator is known to be "heteroskedasticity-consistent", but it is less\nwell-known to be "nonlinearity-consistent'' as well. Nonlinearity, however,\nraises fundamental issues because in its presence regressors are not ancillary,\nhence can't be treated as fixed.\n The consequences are deep: (1)~population slopes need to be re-interpreted as\nstatistical functionals obtained from OLS fits to largely arbitrary joint\n xy~distributions; (2)~the meaning of slope parameters needs to be rethought;\n(3)~the regressor distribution affects the slope parameters; (4)~randomness of\nthe regressors becomes a source of sampling variability in slope estimates;\n(5)~inference needs to be based on model-robust standard errors, including\nsandwich estimators or the xy~bootstrap. In theory, model-robust and\nmodel-trusting standard errors can deviate by arbitrary magnitudes either way.\nIn practice, significant deviations between them can be detected with a\ndiagnostic test.\n