Robust Estimation and Tests based on Quadratic Inference Function
Robust estimators and tests based on the quadratic inference function (QIF) are considered. The QIF enables one to combine a set of extended score functions efficiently. For example, one can create an adaptive estimator between the mean and median that is fully efficient at the normal model but is highly robust, with a 25% asymptotic breakdown point. In addition to providing robust point estimators and chi-square tests of parametric hypotheses, one obtains a chi-square goodness of fit statistic for the modeling hypotheses (for example, are the mean and the median of the distribution the same?). We consider a variety of applications of this method. These results are illustrated with a numerical study using both continuous and discrete data.
Key Words and Phrases: Quadratic inference function; Maximum likelihood; M-estimation; Influence function; Breakdown point.