Robust Statistical Methods

During the last nine years, several problems in the statistical processing of biomedical data have been encountered by the author. These problems had in common the fact that most of the usual assumptions were without any solid basis. Poor quality samples drawn from unknown distributions, usually non-normal and frequently non-stationary, were the ordinary lot; nevertheless, sophisticated parameters had to be reliably estimated and the scatter of the estimators was needed to permit comparison of the results. This has been partly solved by application of robust methods.
The methods presented in this text are oriented toward the design of robust estimators. The primary concern is preventing any significant offset of the estimates due to the selection of an erroneous model or to spurious data in the sample. The second concern is bias reduction and variance estimation. The special emphasis reserved to type M estimators is justified by their analytical form which permits to assess their properties, even for small sample sizes (n=10 or 50), without resorting to involved arguments.
The theoretical tools are mainly the jackknife and the influence function. Applied derivations are in the fields of location estimation and regression analysis. Due attention is devoted to computational aspects.