Sensitivity analysis of $M$-estimators of non-linear regression models
Rubio, Asunción ; Quintana, Francisco ; Víšek, Jan Ámos
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 111-125 / Harvested from Czech Digital Mathematics Library
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An asymptotic formula for the difference of the $M$-estimates of the regression coefficients of the non-linear model for all $n$ observations and for $n-1$ observations is presented under conditions covering the twice absolutely continuous $\varrho$-functions. Then the implications for the $M$-estimation of the regression model are discussed.

Publié le : 1994-01-01
Classification:  62F12,  62F35,  62J02 
@article{118646,
     author = {Asunci\'on Rubio and Francisco Quintana and Jan \'Amos V\'\i \v sek},
     title = {Sensitivity analysis of $M$-estimators of non-linear regression models},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {111-125},
     zbl = {0794.62022},
     mrnumber = {1292588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118646}
}

Rubio, Asunción; Quintana, Francisco; Víšek, Jan Ámos. Sensitivity analysis of $M$-estimators of non-linear regression models. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 111-125. http://gdmltest.u-ga.fr/item/118646/

Chatterjee S.; Hadi A.S. Sensitivity Analysis in Linear Regression, J. Wiley & Sons, New York. | MR 0939610 | Zbl 0648.62066

Cook R.D.; Weisberg S. Residuals and Influence in Regression, Chapman and Hall, New York. | MR 0675263 | Zbl 0564.62054

Hampel F.R.; Ronchetti E.M.; Rousseeuw P.J.; Stahel W.A. Robust Statistics - The Approach Based on Influence Functions, J. Wiley & Sons, New York. | MR 0829458 | Zbl 0733.62038

Huber P.J. A robust version of the probability ratio test, Ann. Math. Statist. 36, 1753-1758. | MR 0185747 | Zbl 0137.12702

Víšek J.Á. Stability of regression model estimates with respect to subsamples, Computational Statistics 7 183-203. | MR 1178353

Welsch R.E. Influence function and regression diagnostics, In: Modern Data Analysis, R.L. Launer and A.F. Siegel, eds., Academic Press, New York, 149-169.

Zvára K. Regression analysis (in Czech), Academia, Prague.