ROBUST MODELS IN PROBABILITY-SAMPLING

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically d esign consistent, regardless of how well the underlying model describe s the population. A sufficient condition is identified for this type o f robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the metho d used to fit it. Included among the internally bias-calibrated models , in addition to the aforementioned linear models, are certain canonic al link generalized linear models and nonparametric regressions constr ucted from them by a particular style of focal likelihood fitting. Oth er models can often be made robust by using a suboptimal fitting metho d. Thus the class of model-based, but design consistent, analyses is e nlarged to include more realistic models for certain types of survey v ariable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.