Article
Keywords:
$M$-estimation of non-linear regression models; the influence points
Summary:
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.
References:
Chatterjee S., Hadi A.S.:
Sensitivity Analysis in Linear Regression. J. Wiley & Sons, New York.
MR 0939610 |
Zbl 0648.62066
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.