A widespread problem in applying regression analysis is the presence of data deficiency. In most surveys a not negligible proportion of data is missing, and sophisticated methods are needed to avoid severely biased estimation. Reviews on this important topic are provided, in particular, by Rao et al. (2008, Chapter 8), Little and Rubin (2002), Toutenburg et al. (2002) and Toutenburg, Fieger and Heumann (2000). Recent developments include, for instance, Toutenburg and Srivastava (1999) and Toutenburg and Srivastava (2004), who discuss corrected estimation of population characteristics from partially incomplete survey data. Toutenburg and Shalabh (2001), Heumann (2004), Shalabh and Toutenburg (2005), Toutenburg and Shalabh (2005), Toutenburg et al. (2006), Toutenburg et al. (2005) and Toutenburg, Srivastava and Shalabh (2006) provide neat methods for handling missing data in linear and nonlinear regression models, while, among others, Strobl, Boulesteix and Augustin (2007) and Svejdar et al. (2007) are concerned with classification under missing data.
The paper is organized as follows: The next section describes our modeling of the replication data. Section 3 adapts the idea of regression calibration to replication data and to quadratic predictors. The application to the MONICA data is reported in Section 4, while Section 5 concludes by sketching some topics for further research.