AISM 54, 261-290

© 2002 ISM

Department of Stochastic Informatics, Institute of
Information Theory and Automation, Academy of Sciences, the Czech
Republic and

Department of Macroeconomics, Institute of Economic Studies, Charles University, Opletalova ulice 26, CZ-110 01 Prague 1, the Czech Republic, e-mail: visek@mbox.fsv.cuni.cz

Department of Macroeconomics, Institute of Economic Studies, Charles University, Opletalova ulice 26, CZ-110 01 Prague 1, the Czech Republic, e-mail: visek@mbox.fsv.cuni.cz

(Received November 16, 1998; revised September 18, 2000)

Abstract. Asymptotic representations of the difference of $M$-estimators of the parameters of nonlinear regression model for the full data and for the subsample of data are given for the following three situation: i) fix number of points excluded from data, ii) increasing number, however asymptotically negligible part of data excluded, and finally iii) asymptotically fix portion of data excluded. Asymptotic normality of the difference of estimators (for the two latter cases) is proved.

Key words and phrases: Sensitivity analysis, asymptotic representation, asymptotic distribution of the difference of M-estimators, testing subsample stability of estimates, scale invariance, diagnostics of subsets of influential points, diversity of estimates.