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.