Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 201--226

ON TWO-TERM EDGEWORTH EXPANSIONS AND BOOTSTRAP APPROXIMATIONS FOR STUDENTIZED MULTIVARIATE $M$-ESTIMATORS

By

SOUMENDRA NATH LAHIRI, Iowa State University

SUMMARY. This paper gives two-term Edgeworth expansions for the noralized $M$-estimators under very mild conditions. With an appropriate choice of the studentizing matrix, it obtains Berry-Esseen Theorems and two-term Edgeworth expansions for studentized multivariate $M$-estimators. Furthermore, it is shown that the bootstrap approximation is second order correct in the studetized case.

AMS subject classification. Primary 62E20; secondary 62E05.

Key words and phrases. Bootstrap, Edgeworth expansion, $M$-estimator, second order optimality, Studentization.

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