Generalized Shrunken-Type Robust Estimation

Abstract

The parameter estimation problem in surveying adjustment is considered when outliers and multicollinearity exist simultaneously. A class of new estimators—generalized shrunken-type robust estimators—are proposed by grafting the biased estimation techniques philosophy into the robust estimator, and their statistical properties are discussed. By appropriate choices of the shrinking parameter matrix, we obtain many useful and important estimators. A numerical example is used to illustrate that these new estimators can not only resist the influence of outliers but also effectively overcome difficulty caused by multicollinearity.