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Diagnostics of regression subsample stability. (English) Zbl 0924.62072
The author investigates the asymptotic representation of the difference of parameter estimators for nonlinear regression. A Bahadur type asymptotic representation of the difference between \(M\)-estimators, i.e. estimators of regression coefficients for the full data set and for the set with one deleted observation, is derived. The proposed representation is invariant with respect to the scale parameter of the model residuals.

62J02 General nonlinear regression
62J20 Diagnostics, and linear inference and regression
62F12 Asymptotic properties of parametric estimators
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)