An algorithm for finding least square generalized inverses for classification models with arbitrary patterns

References

• Birkes , D , Dodge , Y and Seely , J . 1976 . Spanning sets for estimable contrasts in classification models . Ann. Statist , 4 : 86 – 107 .
   Web of Science ®Google Scholar
• Bose , R.C . 1949 . “ Least square aspects of analysis of variance ” . In Inst. Stat , 9 N.C : Chapel Hill . Mimeo
   Google Scholar
• Calinski , T . 1971 . On some desirable patterns in block designs . Biometrics , 27 : 275 – 292 .
   Web of Science ®Google Scholar
• Eccleston , J.A and Hedayat , A . 1974 . On the theory of connected designs: characterisation and optimality . Ann.Statist , 2 : 1238 – 1255 .
   Web of Science ®Google Scholar
• Mitra , S.K and Bhimasankaram , P . 1971 . Generalized inverse of partitioned matrices and recalculation of least square estimates for data or model changes . Sankhya , 33 : 395 – 410 .
   Google Scholar
• Rao , C.R . 1962 . A note on generalized inverse of a matrix with applications to problems in mathematical statistics . J. Royal Statist. Soc , 24 : 152 – 158 .
   Google Scholar
• Rao , C.R . 1967 . Calculus of generalized inverse of matrices, Part I: General theory . Sankhya , 29 : 317 – 342 .
   Google Scholar
• Rao , C.R and Mitra , S.K . 1971 . Generalized Inverses of Matrices and its Applications , New York : Wiley .
   Google Scholar
• Srivastava , J.N and Anderson , D.A . 1970 . Some basic properties of multidimensional partially balanced designs . Ann. Math. Statist , 41 : 1438 – 1445 .
   Google Scholar
• Weeks , D.L and Williams , D.R . 1964 . A note on determination of connectedness in an N- way cross classification . Technometrics , 6 errata Technometrics, 7, 281
   Google Scholar