Model robust confidence intervals using maximum likelihood estimators. (English) Zbl 0596.62032

Royall, Richard M.

Int. Stat. Rev. 54, 221-226 (1986).

Summary: Standard large-sample confidence intervals about a maximum likelihood estimator \({\hat \theta}\) are two-thirds robust; i.e. when the parametric model is imperfect \({\hat \theta}\) often remains consistent and asymptotically normal. The confidence intervals are invalidated only because the third necessary condition, consistency of the variance estimator, fails. The ’delta method’ provides a simple alternative variance estimator which remains consistent under more general conditions and provides robust large-sample confidence intervals.

MSC:

62F35	Robustness and adaptive procedures (parametric inference)
62F25	Parametric tolerance and confidence regions

Keywords:

robustness; large-sample theory; maximum likelihood estimator; consistent; asymptotically normal; delta method; variance estimator