Robust estimation of non-linear aspects
نویسنده
چکیده
As a rst step for dealing with eecient robust estimation in non-linear models , we regard the problem of eecient robust estimation of non-linear aspects (functions) '() of the unknown parameter of a linear model. For robust estimation of a general non-linear aspect we propose estimators which are based on one-step-M-estimators and derive their asymptotic behaviour at the contaminated linear model, where the errors have contaminated normal distributions. The asymptotic behaviour provides criteria for robustness and optimality of the estimators and the corresponding designs. Because it is impossible to nd globally optimal robust estimators and designs locally optimal solutions are used for eeciency comparisons. Simple formulas for the eeciency rates are given for the general case. Using these results the eeciency rates for estimating robustly the relative variation of a circadian rhythm are calculated. These eeciency rates are very similar to those for non-robust estimation although on principle there is an important diierence.
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