Bootstrapping \(M\)-estimators of a multiple linear regression parameter
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.
scientific article; zbMATH DE number 150377