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Original Articles

Harmonic mean approach to uunbalanced random effects models under heteroscedasticity

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Pages 1261-1286 | Published online: 27 Jun 2007

References

  • Bush , N. and Anderson , R.L. 1963 . A comparison of three different procedures for estimating variance components . Technometrics , 5 : 421 – 440 .
  • Cornstock , R.E. and Robinson , H.J. 1348 . The components ef genetic variance in populations of biparental progenies and their use in estimating the average degree of dominance . Biometrics , 4 : 252 – 266 .
  • Davis , A.W. 1976 . Statistical distributions in univariate and multivariate Edgeworth populations . Biometrika , 63 : 661 – 670 .
  • Gideon , R.A. and Gurland , J. 1977 . Some alternative expansions for the distribution function of a noncentral chi-square random variable . SIAM J. of Math. Analy , 8 : 100 – 110 .
  • 1956A . Distribution of definite and of indefinite quadratic form . Ann. Math. Statist , 26 : 122 – 127 .
  • Gurland , J. 1956B . Quadratic forms in normally distributed random variables . Sankhya , 17 : 37 – 50 .
  • Kendall , M.G. and Stuart , A. 1977 . “ The Advanced Theory of Statistics ” . Vol. I , London : Griffin .
  • Kotz , S. , Johnson , N.L. and Boyd , D.W. 1967A . Series representations of distributions of quadratic forms in normal variables . Ann. Math. Statist , 38 : 823 – 837 . I. Central case
  • Kotz , S. , Johnson , N.L. and Boyd , D.W. 1967B . Series representations of distributions of quadratic forms in normal variables. II . Ann. Math. Statist , 38 : 838 – 848 . Non-central case
  • Rankin , N.O. 1974 . The harmonic mean method for one-way and two-way analyses of variance . Biometrika , 61 : 117 – 122 .
  • Satterthwaite , F.E. 1946 . An approximate distribution of estimates of variance components . Biometrics , 2 : 110 – 114 .
  • Scheffe , H. 1959 . “ The Analysis of Variances ” . New York : John Wiley .
  • Searle , S.R. 1971 . “ Linear Models ” . New York : John Wiley .
  • Tan , W.Y. 1977 . On the distribution of second degree polynomial in normal random variables . Canadian J. Statist , 5 : 241 – 250 .
  • Tan , W.Y. 1979 . On the quadratic estimation of covariance matrix in multivariate linear models . J. Multivar. Analy , 5 : 452 – 459 .
  • Tan , W.Y. 1982a . On comparing several straight lines under heteroscedasticity and robustness with respect to departure from normality . Commun. Statist. , A ( 11 ) : 731 – 751 .
  • Tan , W.Y. 1982b . On approximating probability distribution of a statistic of Brown-Forsythe from normal and non-normal univers . J. Statist. Comput. Simul. , 16 ( 11 ) : 35 – 55 .
  • Tan , W.Y. 1982c . Sampling distributions of t, F and variance ratio in two samples &ANOVA models and robustness with respect to departure from normality . Commun. Statist , A ( 11 ) : 2482 – 2513 . Special issue on robustness
  • Tan , W.Y. and Cheng , S.S. 1981 . Cumulants of bilinear forms and quadratic forms and its applications . Commun. Statist , A ( 10 ) : 283 – 298 .
  • Tan , W.Y. and Cheng , S.S. 1984 . On testing variance components in three stages nested random effects models . Sankhya , 3 ( 48 ) : 188 – 200 .
  • Tan , W.Y. and Wong , S.P. 1977 . On the Roy--Tiku approximation to the distributions of sample variances from nonnormal univer . J. Amer. Statist. Assoc , 72 ( 48 ) : 875 – 881 .
  • Tan , W.Y. 1978 . On approximating the central and non-central multivariate gamma distributio . Commun. Statist , B7 ( 48 ) : 227 – 243 .
  • Tan , W.Y. and Wong , S.P. 1980 . On approximating the null and non-null distributions of the F-ratio in unbalanced random effect models from non-normal universe . J. Amer. Statist. Assoc , 75 ( 48 ) : 652 – 665 .
  • Tiku , M.L. 1964 . Approximating the general non-normal variance-ratio sampling distributions . Biometrika , 51 ( 48 ) : 83 – 95 .
  • Tiku , M.L. 1965 . Laguerre series forms of non-central x2 and F distributions . Biometrika , 52 ( 48 ) : 415 – 427 .
  • Tiku , M.L. 1975 . “ Languerre series forms of the distributions of classical test-statistics and their robustness in non-normal situations, in ” . In Applied Statistics Edited by: Gupta , R.P. New York

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