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

Karabulut, I; Lahiri, SN

doi:10.1017/s1446788700001063

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

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, cilt.62, ss.361-370, 1997 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 62
Basım Tarihi: 1997
Doi Numarası: 10.1017/s1446788700001063
Dergi Adı: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.361-370
Gazi Üniversitesi Adresli: Hayır

Özet

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.