Robust Scale Estimation and Hypothesis Testing based on Quadratic Inference Function
The standard deviation is the most common estimator of scale, but it is known to lack resistance and robustness. In this paper, we propose a new scale estimator based on the quadratic inference function (QIF). This estimator is efficient, robust and possesses a reasonable breakdown point. In addition to obtaining parameter estimators, we develop $\chi^2$ tests of parametric hypotheses such as a test of the equality of variances in the k-sample case. Monte Carlo experiments suggest that this new method is reasonably robust for departures from normality and for contaminated samples. We compare the performance of this new method with other well-known methods by Monte Carlo simulation.
Key Words and Phrases: Quadratic inference function; Maximum likelihood; M-estimation; Influence function; Breakdown point.