A centered Gaussian with smaller covariance assigns at least as much probability as one with larger covariance to any closed convex set with reference probability at least 1/2.
Models as Approximations I: Consequences Illustrated with Linear Regression
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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 can't be treated as fixed. The consequences are deep: (1)~population slopes need to be re-interpreted as statistical functionals obtained from OLS fits to largely arbitrary joint $\xy$~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; (5)~inference needs to be based on model-robust standard errors, including sandwich estimators or the $\xy$~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.
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2026 2representative citing papers
Stochastic sensitivity analysis for matched studies finds worst-case conditional laws for hidden confounders instead of worst-case realizations, controlled by a sensitivity parameter that permits imperfect alignment with potential outcomes and yields higher robustness than conventional methods.
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Gaussian comparison above the median
A centered Gaussian with smaller covariance assigns at least as much probability as one with larger covariance to any closed convex set with reference probability at least 1/2.
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Stochastic Sensitivity Analysis for Matched Observational Studies
Stochastic sensitivity analysis for matched studies finds worst-case conditional laws for hidden confounders instead of worst-case realizations, controlled by a sensitivity parameter that permits imperfect alignment with potential outcomes and yields higher robustness than conventional methods.