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Teacher's Corner

An Accessible Proof of Craig's Theorem in the General Case

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Pages 59-62 | Received 01 Nov 1993, Published online: 27 Feb 2012

References

  • Buoko-Krasnicka , B. 1991 . “Stochastic Independence of Two Quadratic Forms in Normally Distributed Variates” , Arizona State University, Dept. of Mathematics . unpublished Master's thesis
  • Craig , A. T. 1943 . “Note on the Independence of Certain Quadratic Forms” . Annals of Mathematical Statistics , 14 : 195 – 197 .
  • Driscoll , M. F. and Gundberg , W. R. Jr. 1986 . “A History of the Development of Craig's Theorem” . The American Statistician , 40 : 65 – 70 .
  • Eaton , M. L. 1983 . Multivariate Statistics: A Vector Space Approach , New York : John Wiley .
  • Laha , R. G. 1956 . “On the Stochastic Independence of Two Second-Degree Polynomial Statistics in Normally Distributed Variates” . Annals of Mathematical Statistics , 27 : 790 – 796 .
  • Mathai , A. M. and Provost , S. B. 1992 . Quadratic Forms in Random Variables: Theory and Applications , New York : Marcel Dekker .
  • Nagase , G. and Bannerjee , K. S. 1976 . “Independence of Second Degree Polynomial Statistics in Normal Variates” . The American Statistician , 30 : 201
  • Ogasawara , T. and Takahashi , M. 1951 . “Independence of Quadratic Quantities in a Normal System” . Journal of Science of the Hiroshima University , 15 : 1 – 9 . Ser. A
  • Ogawa , J. 1950 . “On the Independence of Quadratic Forms in a Non-Central Normal System” . Osaka Mathematical Journal , 2 : 151 – 159 .
  • Ogawa , J. 1993 . “A History of the Development of Craig-Sakamoto's Theorem Viewed from Japanese Standpoint” . Proceedings of the Institute of Statistical Mathematics , 41 : 47 – 59 . (in Japanese and English)
  • Reid , J. G. and Driscoll , M. F. 1988 . “An Accessible Proof of Craig's Theorem in the Noncentral Case” . The American Statistician , 42 : 139 – 142 .
  • Scarowsky , I. 1973 . “Quadratic Forms in Normal Variables” , McGill University, Dept. of Mathematics . unpublished Master's thesis
  • Searle , S. 1971 . Linear Models , New York : John Wiley .

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