30
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Contributions to-asymptotic theory in regression models with linear covariance structureFootnote1

&
Pages 243-269 | Published online: 27 Jun 2007

References

  • Rao , C.R. 1970 . Estimation of heteroscedastic variances in linear models . J. Amer. Statist, Assoc , 65 : 161 – 172 .
  • Rao , C.R. 1971 . Estimation of variance and covariance components -Minque theory . J. Multiv. Anal , 1 : 257 – 275 .
  • Rao , C.R. 1971 . Minimum variance quadratic unbiased estimation of variance components . J. Multiv. Anal , 1 : 445 – 456 .
  • Rao , C.R. 1972 . Estimation of variance and covariance components in linear models . J, Amer, Statist, Assoc , 67 : 112 – 115 .
  • Lamotte , L.R. 1973 . Quadratic estimation of variance components . Biometrics , 29 : 311 – 330 .
  • Hartley , H.O. , Rao , J.N.K. and Lamotte , L.R. 1978 . A simple ‘synthesis’-based method of variance component estimation . Biometrics , 34 : 233 – 242 .
  • Anderson , T.W. “ Estimation of covariance matrices which are linear combinations or whose inverses are linear combinations of given matrices ” . In Essays in Probability and Statistics , Chapel Hill : Univ. of North Carolina Press .
  • Anderson , T.W. 1973 . Asymptotically efficient estimation of covariance matrices with linear structure . Ann. Statist , 1 : 135 – 141 .
  • Humak , K.M.S. 1977 . “ Statistische Methoden der Modellbildung ” . In Bd. 1: Statistische Inferenz für lineare Parameter , Berlin : Akademie-Verlag . to appear
  • Miller , J.J. 1977 . Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance . Ann. Statist , 5
  • Miller , J.J. 1973 . Asymptotic properties and computation of maximum likelihood estimates in the mixed model of the analysis of variance , Stanford Univ . Technical Report No. 12, Department of Statistics
  • Brown , K.G. 1976 . Asymptotic behaviour of Minque-type estimators of variance components . Ann. Statist , 4 : 746 – 754 .
  • Jennrich , R.I. 1969 . Asymptotic properties of non-linear least squares estimators . Ann. Math. Statist , 40 : 633 – 643 .
  • Bunke , H. and Schmidt , W.H. 1980 . Asymptotic results on nonlinear approximation of regression functions and weighted least squares . Math. Operationsforsch. Statist., Ser. Statistics , 11 : 3 – 22 .
  • Schmidt , W.H. 1979 . Asymptotic results for estimation and testing variances in regression models . Math. Operationsforsch. Statist., Ser. Statistics , 10 : 209 – 236 .
  • Ivanov , A.Y. 1976 . An asymptotic expansion for the distribution of the least squares estimator of the non-linear regression parameter . Theory Prob. and Applic , XXI : 557 – 570 .
  • Chanda , K.C. 1976 . Efficiency and robustness of least squares estimators . Sankhya B , 38 : 153 – 163 .
  • Chow , Y.S. 1967 . On the strong law of large numbers for martingales . Annt Math. Statist , 38 : 610
  • Eicker , F. 1966 . A multivariate central limit theorem for random linear vector forms . Ann. Math. Statist , 37 : 1825 – 1828 .
  • Schmidt , W.H. 1975 . Asymptotic normality of Least-Squares estimators in multivariate singular linear models . Math. Operationsf. Statist , 6 : 285 – 299 .
  • Le Cam , L. On the asymptotic theory of estimation and testing hypotheses . Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability . Vol. I , pp. 129 – 156 .
  • Bahadur , R.R. 1964 . On Fisher's bound for asymptotic variances . Ann. Math. Statist , 35 : 1545 – 1552 .
  • Bahadur , R.R. 1968 . Rates of convergence of estimates and test statistics . Ann. Math. Statist , 39 : 303 – 324 .
  • Kruskal , W. 1968 . When are Gauss-Markov and least-souares estimators identical? A coordinate free approach . Ann. Math. Statist , 39 : 70 – 75 .
  • Zwanzig , S. 1980 . The choice of approximative models in nonlinear regression . Math,. Operationsf. Statist., Set. Statistics , 11 : 23 – 47 .
  • Willers , R. 1978 . “ Schwache Konsistenz von Kleinste-Quadrate Schätzern für Regressions- und Streuungsparameter in linearen Modellen ” . In Diss , Univ. Dortmund .
  • Drygas , H. 1971 . Consistency of the least squares and Gauss-Markov estimators in regression models . Z, Wahrscheinlichkeitstheorie verw. Geb , 17 : 309 – 326 .
  • Drygas , H. 1976 . Weak and strong consistency of the least squares estimator in regression models . Z. Wahrscheinlichkeitstheorie verw. Geb , 34 : 119 – 127 .
  • Kleffe , J. 1977 . Invariant Methods for estimating variance components in mixed linear models . Math. Operationsforsch. Statist., Ser. Statistics , 8 : 233 – 250 .
  • Kleffe , J. 1976 . A Note on Minque for Normal Models . Math. Operationsforsch. Statist , 7 : 707 – 714 .
  • Searle , S.R. 1970 . Large sample variances of maximum likelihood estimators of variance components using unbalanced data . Biometrics , 26 : 505 – 524 .
  • Thrum , R. On equivalence of weak and L2 consistency of quadratic forms under normality . V. International Conf. on Math. Statistics, Wisla. Abstracts .
  • Anderson , T.W. and Taylor , J.B. 1976 . Strong consistency of least squares estimates in normal linear regression . Ann. Statist , 4 : 788 – 790 .
  • Drygas , H. 1975 . A note on a paper by T. Kloek concerning the consistency of variance estimation in the linear model . Econometrica , 43
  • Schmidt , W. 1976 . Strong consistency of variance estimation and asymptotic theory for tests of the linear hypothesis in multivariate linear models . Math. Ope-rationsforsch. Statist , 7 : 701 – 705 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.