Sensitivity analysis of \(M\)-estimates of nonlinear regression model: Influence of data subsets. (English) Zbl 1013.62072

Víšek, Jan Ámos

Ann. Inst. Stat. Math. 54, No. 2, 261-290 (2002).

Summary: Asymptotic representations of the difference of \(M\)-estimators of parameters of nonlinear regression models for full data and for subsamples of data are given for the following three situations: i) fix number of points excluded from the 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.

MSC:

62J02	General nonlinear regression
62J20	Diagnostics, and linear inference and regression
62F12	Asymptotic properties of parametric estimators

Keywords:

sensitivity analysis; asymptotic representation; asymptotic distribution of difference of M-estimators; testing subsample stability of estimates; scale invariance; diagnostics of subsets of influential points; diversity of estimates