Two-term edgeworth expansion for M-estimators of a linear regression parameter without Cramer-type conditions and an application to the bootstrap


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Karabulut I., Lahiri S.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol.62, pp.361-370, 1997 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62
  • Publication Date: 1997
  • Doi Number: 10.1017/s1446788700001063
  • Title of Journal : JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
  • Page Numbers: pp.361-370

Abstract

A two-term Edgeworth expansion for the distribution of an M-estimator of a simple linear regression parameter is obtained without assuming any Cramer-type conditions. As an application, it is shown that certain modification of the naive bootstrap procedure is second order correct even when the error variables have a lattice distribution. This is in marked contrast with the results of Singh on the sample mean of independent and identically distributed random variables.