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Reduced Bias and Increased Variance: A Possible Trade-off in Calibration for Non-response Treatment

Keywords: Star vector, moon vector, Bottom-up, Top-down

In this paper we present estimators of a population total based on the well-known calibration technique, used here to compensate for non-response in a given random sample. These estimators use auxiliary information. We consider two types of auxiliary variable. For the first type we have access to totals known at the population level; for the second type we have information at the sample level only. This leads to several possibilities for calibration. Should one use all available information in one direct calibration, or should one divide the calibration procedure into two steps, and in the latter case, in what order should the two types of information be entered? Furthermore, it is not obvious that the second step of the procedure should necessarily use all of the available information. In examining the properties of the resulting estimators, we are particularly interested in a possible trade-off between reduced bias and increased variance: Is increased variance the price one would always have to pay for a reduced bias? Properties of estimators will be examined by a small simulation study.