  In the presence of auxiliary information, model-assisted estimators use a
working model that links the variable of interest and the auxiliary variables
in order to improve the Horvitz-Thompson estimator. The resulting estimators
are asymptotically design unbiased and asymptotically more efficient than the
Horvitz-Thompson estimator under some regularity conditions and for a wide
range of working models. In this work, we adapt model-assisted total estimators
to missing at random data building on the idea of nonresponse weighting
adjustment. We consider nonresponse as a second phase of the survey and
reweight the units in model-assisted estimators using the inverse of estimated
response probabilities in order to compensate for the nonrespondents. We
develop the asymptotic properties and discuss calibration of the weights of our
proposed estimators. We provide formulae for asymptotic variance and variance
estimators. We conduct a simulation study that describes the behavior of the
proposed estimators.
