## Bootstrapping $$M$$-estimators of a multiple linear regression parameter.(English)Zbl 0792.62058

This paper considers a multiple linear regression model $$Y_ i= X_ i' \beta+\varepsilon_ i$$, where the errors $$\varepsilon_ i$$ are independent random variables with common distribution $$F$$ and the $$X_ i$$ are known design vectors. Let $$\overline{\beta}_ n$$ be the $$M$$- estimator of $$\beta$$ corresponding to a score function $$\psi$$. Two-term Edgeworth expansions for the distributions of standardized and Studentized $$\overline{\beta}_ n$$ are obtained under some conditions on $$F$$, $$\psi$$ and the design. Also, it is shown that the bootstrap method is second order correct.

### MSC:

 62J05 Linear regression; mixed models 62G09 Nonparametric statistical resampling methods 62F10 Point estimation 62E20 Asymptotic distribution theory in statistics
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