A Comparison of Two Criteria for Ordinary-Least-Squares Estimators to Be Best Linear Unbiased Estimators

References

• Alalouf , I. S. and Styan , George P. H. 1983 . “Characterizations of the Conditions for the Ordinary Least Squares Estimator to Be Best Linear Unbiased” . In Topics in Applied Statistics , Edited by: Chaubey , Y. P. and Dwivedi , T. D. 331 – 344 . Montreal : Concordia University .
   Google Scholar
• Anderson , T. W. 1948 . “On the Theory of Testing Serial Correlation” . Skandinavisk Aktuarietidskrift , 31 : 88 – 116 .
   Google Scholar
• Baksalary , J. K. and Kala , R. 1983 . “On Equalities Between BLUEs, WLSEs, and SLSEs” . The Canadian Journal of Statistics , 11 : 119 – 123 . Correction (1984), 12, 240
   Google Scholar
• Farebrother , R. W. 1985 . “McElroy's Condition” . The American Statistician , 39 : 240 (letter to the editor)
   Web of Science ®Google Scholar
• Feuerverger , A. and Fraser , D. A. S. 1980 . “Categorical Information and the Singular Linear Model” . The Canadian Journal of Statistics , 8 : 41 – 45 .
   Google Scholar
• Goldman , A. J. and Zelen , M. 1964 . “Weak Generalized Inverses and Minimum Variance Unbiased Estimation” . Journal of Research of the National Bureau of Standards , 68 : 151 – 172 . Sec. B
   Google Scholar
• Haberman , Shelby J. 1975 . “How Much Do Gauss-Markov and Least Square Estimates Differ? A Coordinate-Free Approach” . The Annals of Statistics , 3 : 982 – 990 .
   Web of Science ®Google Scholar
• Kempthorne , Oscar . 1980 . “The Term Design Matrix” . The American Statistician , 34 : 249 (letter to the editor)
   Web of Science ®Google Scholar
• Magness , T. A. and McGuire , J. B. 1962 . “Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters” . Annals of Mathematical Statistics , 33 : 462 – 470 .
   Google Scholar
• Mathew , Thomas . 1986 . “McElroy's Condition: Comments on Milliken and Albohali and Farebrother” . The American Statistician , 40 : 179 (letter to the editor)
   Web of Science ®Google Scholar
• McElroy , F. W. 1967 . “A Necessary and Sufficient Condition That Ordinary Least-Squares Estimators Be Best Linear Unbiased” . Journal of the American Statistical Association , 62 : 1302 – 1304 .
   Web of Science ®Google Scholar
• Milliken , George A. and Albohali , Mohammed . 1984 . “On Necessary and Sufficient Conditions for Ordinary Least Squares Estimators to Be Best Linear Unbiased Estimators” . The American Statistician , 38 : 298 – 299 .
   Web of Science ®Google Scholar
• Norlèn , Urban . 1975 . “The Covariance Matrices for Which Least Squares Is Best Linear Unbiased” . Scandinavian Journal of Statistics , 2 : 85 – 90 .
   Google Scholar
• Odell , Patrick L. 1983 . “Gauss-Markov Theorem” . In Encyclopedia of Statistical Sciences, Vol. 3: Faà di Bruno's Formula to Hypothesis Testing , Edited by: Kotz , S. , Johnson , N. L. and Read , C. B. 314 – 316 . New York : John Wiley .
   Google Scholar
• Puntanen , Simo . 1986 . “Further Comments on Milliken and Albohali” . The American Statistician , 40 : 178 (letter to the editor)
   Google Scholar
• Puntanen , Simo . 1987 . “On the Relative Goodness of Ordinary Least Squares Estimation in the General Linear Model” , Ph.D. dissertation Vol. 216 , Acta Universitatis Tamperensis . Ser. A
   Google Scholar
• Puntanen , Simo and Styan , George P. H. 1988 . “On the Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator” unpublished manuscript submitted to The American Statistician.
   Google Scholar
• Rao , Radhakrishna C. “Least Squares Theory Using an Estimated Dispersion Matrix and Its Applications to Measurement of Signals” . Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1) . Edited by: LeCam , L. M. and Neyman , J. pp. 355 – 372 . Berkeley : University of California Press .
   Google Scholar
• Rao , Radhakrishna C. 1976 . “Unified Theory of Linear Estimation” . Sankhyā , 139 : 371 – 394 . Ser. A, Corrigenda (1972), 34, 194 and 477
   Google Scholar
• Rao , Radhakrishna C. 1973 . Linear Statistical Inference and Its Applications, , 2nd ed. , New York : John Wiley .
   Google Scholar
• Searle , S. R. 1971 . Linear Models , New York : John Wiley .
   Google Scholar
• Searle , S. R. 1985 . “Comment on Milliken and Albohali” . The American Statistician , 39 : 240 (letter to the editor)
   Web of Science ®Google Scholar
• Shelton , John T. and Lowe , Victor W. 1986 . “Comment on Milliken and Albohali” . The American Statistician , 40 : 78 – 79 . (letter to the editor)
   Google Scholar
• Styan , George P. H. 1983 . “Generalized Inverses” . In Encyclopedia of Statistical Sciences, Vol. 3: Faà di Bruno's Formula to Hypothesis Testing , Edited by: Kotz , S. , Johnson , N. L. and Read , C. B. 334 – 337 . New York : John Wiley .
   Google Scholar
• Weiss , Robert and Lavine , Michael . 1986 . “Necessary and Sufficient Conditions for Ordinary Least Squares Estimators to Be Best Linear Unbiased Estimators” . The American Statistician , 40 : 178 – 179 . (letter to the editor)
   Web of Science ®Google Scholar
• Zyskind , G. 1962 . “On Conditions for Equality of Best and Simple Linear Least Squares Estimators” . Annals of Mathematical Statistics , 33 : 1502 – 1503 .
   Google Scholar
• Zyskind , G. 1967 . “On Canonical Forms, Non-negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models” . Annals of Mathematical Statistics , 38 : 1092 – 1109 .
   Google Scholar
• Zyskind , G. 1969 . “Parametric Augmentations and Error Structures Under Which Certain Simple Least Squares and Analysis of Variance Procedures Are Also Best” . Journal of the American Statistical Association , 64 : 1353 – 1368 .
   Web of Science ®Google Scholar