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Original Articles

Simultaneous Confidence Bands for Regression With Unknown Unequal Variances

Pages 173-186 | Published online: 12 Mar 2012

REFERENCES

  • Amemiya , T. 1973 . “Regression Analysis When the Variance of the Dependent Variable Is Proportional to the Square of Its Expectation,” . Journal of the American Statistical Association , 68 : 928 – 934 .
  • Banerjee , S. K. 1960 . “Approximate Confidence Interval for Linear Functions of Means of k-Population When the Populations Are Not Equal,” . Sankhya , 22 : 357 – 358 .
  • Carroll , R. 1982 . “Adapting for Heteroscedasticity in Linear Models,” . The Annals of Statistics , 10 : 1224 – 1233 .
  • Carroll , R. J. and Cline , D. B. H. 1988 . “An Asymptotic Theory for Weighted Least Squares With Weights Estimated by Replication,” . Biometrika , 75 : 35 – 44 .
  • Cochran , W. G. and Carroll , S. P. 1953 . “A Sampling Investigation of the Efficiency of Weighting Inversely as the Estimated Variance,” . Biometrics , 9 : 447 – 459 .
  • Cohen , M. L. , Dalal , S. R. and Tukey , J. W. 1984 . “Robust Smoothly-Heterogeneous Variance Regression,” Morristown , NJ : Bell Communications Research. . technical memorandum
  • Dalai , S. R. 1978 . “Simultaneous Confidence Procedures for Univariate and Multivariate Behrens-Fisher Type Problems,” . Biometrika , 65 : 221 – 225 .
  • Dalai , S. R. 1983 . “Exact Simultaneous Confidence Bands for Ran dom Intercept Regression,” . Technometrics , 25 : 263 – 269 .
  • Dalai , S. R. and Fortini , P. 1982 . “An Equality Comparing Sums and Maxima With Application to Behrens–Fisher Type Problems,” . The Annals of Statistics , 10 : 297 – 301 .
  • Dunnett , C. W. 1980 . “Pairwise Multiple Comparisons in the Unequal Variance Case,” . Journal of the American Statistical Association , 75 : 796 – 800 .
  • Graybill , F. A. 1961 . An Introduction to Linear Statistical Models New York : McGraw-Hill. .
  • Hahn , G. J. and Hendrickson , R. W. 1971 . “A Table of Percentage Points of the Distribution of the Largest Absolute Value of kStudent tVariates and Its Applications,” . Biometrika , 58 : 323 – 332 .
  • Hedges , L. V. and Olkin , I. 1985 . Statistical Methods for Meta-Analysis New York : Academic Press. .
  • Meier , P. 1953 . “Variance of a Weighted Mean,” . Biometrics , 9 : 59 – 73 .
  • Miller , R. G. 1980 . Simultaneous Statistical Inference, , 2nd ed. New York : Springer-Verlag. .
  • Mosteller , F. and Tukey , J. W. 1982 . “Combinations of Results of Stated Precision, I: The Optimistic Case,” . Utilitas Mathematica, Ser. A , 21 : 155 – 158 .
  • Mosteller , F. and Tukey , J. W. 1984 . “Combinations of Results of Stated Precision, II: A More Realistic Case”. ” . In W. G. Cochran's Impact on Statistics Edited by: Rao , P. S. R. S. and Sedransk , J. 223 – 252 . New York : John Wiley. .
  • Naiman , D. Q. 1987 . “Minimax Regret Simultaneous Confidence Bands for Multiple Regression Functions,” . Journal of the American Statistical Association , 82 : 894 – 901 .
  • Nelson , W. 1971 . “Graphical Analysis of Accelerated Life Test Data With the Inverse Power Law Model,” . IEEE Transactions on Reliability , 21 : 2 – 11 .
  • Paull , A. E. 1950 . “On a Preliminary Test for Pooling Mean Squares in the Analysis of Variance,” . The Annals of Mathematical Statistics , 21 : 539 – 556 .
  • Rutemiller , H. C. and Bowers , D. A. 1968 . “Estimation in a Heteroscedastic Regression Model,” . Journal of the American Statistical Association , 63 : 552 – 557 .
  • Üsidáak , Z. 1967 . “Rectangular Confidence Region for the Means of Multivariate Normal Distributions,” . Journal of the American Statistical Association , 62 : 626 – 633 .
  • Tamhane , A. C. 1977 . “Multiple Comparisons in Model I One-Way ANOVA With Unequal Variances,” . Communications in Statistics, Part A—-Theory and Methods , 1 : 15 – 32 .
  • Tong , Y. L. 1980 . Probability Inequalities in Multivariate Distributions New York : Academic Press. .

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