Asymptotic Expansion and Conditional Robustness for the Sample Multiple Correlation Coefficient Under Nonnormality

References

• Algina , J. ( 1999 ). A comparison of methods for constructing confidence intervals for the squared multiple correlation coefficient . Multivariate Behav. Res. 34 : 493 – 504 . [CSA]
   PubMed Web of Science ®Google Scholar
• Algina , J. , Olejnik , S. ( 2000 ). Determining sample size for accurate estimation of the squared multiple correlation coefficient . Multivariate Behav. Res. 35 : 119 – 136 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Algina , J. , Olejnik , S. ( 2003 ). Sample size tables for correlation analysis with applications in partial correlation and multiple regression analysis . Multivariate Behav. Res. 38 : 309 – 323 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Anderson , T. W. ( 1958 ). An Introduction to Multivariate Statistical Analysis . New York : Wiley .
   Google Scholar
• Anderson , T. W. ( 2003 ). An Introduction to Multivariate Statistical Analysis , 3rd . ed. New York : Wiley .
   Google Scholar
• Ding , C. G. ( 1994 ). On the computation of the noncentral beta distribution . Computat. Statist. Data Anal. 18 : 449 – 455 . [CSA] [CROSSREF]
   Google Scholar
• Ding , C. G. ( 1996 ). On the computation of the distribution of the square of the sample multiple correlation coefficient . Computat. Statist. Data Anal. 22 : 345 – 350 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Fisher , R. A. ( 1928 ). The general sampling distribution of the multiple correlation coefficient . Proc. Roy. Soc. London A 121 : 654 – 673 . [CSA]
   Google Scholar
• Fujikoshi , Y. ( 1980 ). Asymptotic expansions for the distributions of the sample roots under nonnormality . Biometrika 67 : 45 – 51 . [CSA]
   Web of Science ®Google Scholar
• Gatsonis , C. , Sampson , A. R. ( 1989 ). Multiple correlation: exact power and sample size calculations . Psychol. Bull. 106 : 516 – 524 . [PUBMED] [INFOTRIEVE] [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Gurland , J. ( 1968 ). A relatively simple form of the distribution of the multiple correlation coefficient . J. Roy. Statist. Soc. B 30 : 276 – 283 . [CSA]
   Google Scholar
• Gurland , J. , Milton , R. ( 1970 ). Further consideration of the distribution of the multiple correlation coefficient . J. Roy. Statist. Soc. B 32 : 381 – 394 . [CSA]
   Google Scholar
• Hall , P. ( 1992 ). The Bootstrap and Edgeworth Expansion . New York : Springer . Corrected printing, 1997 .
   Google Scholar
• Lawley , D. N. , Maxwell , A. E. (1971). Factor Analysis as a Statistical Method , 2nd ed.. London : Butterworths.
   Google Scholar
• Lee , Y. S. ( 1971 ). Some results on the sampling distribution of the multiple correlation coefficient . J. Roy. Statist. Soc. B 33 : 117 – 130 . [CSA]
   Google Scholar
• Lee , Y. S. ( 1972 ). Tables of upper percentage points of the multiple correlation coefficient . Biometrika 59 : 175 – 189 . [CSA]
   Web of Science ®Google Scholar
• Magnus , J. R. , Neudecker , H. ( 1999 ). Matrix Differential Calculus with Applications in Statistics and Econometrics , (rev. ed.). New York: Wiley .
   Google Scholar
• Mendoza , J. , Stafford , K. L. ( 2001 ). Confidence intervals, power calculation, and sample size estimation for the squared multiple correlation coefficient under the fixed and random regression models: a computer program and useful standard tables . Educat. Psychol. Measure. 61 : 650 – 667 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Muirhead , R. J. ( 1982 ). Aspects of Multivariate Statistical Theory . New York : Wiley .
   Google Scholar
• Ogasawara , H. ( 2004 ). Asymptotic biases in exploratory factor analysis and structural equation modeling . Psychometrika 69 : 235 – 256 . [CSA]
   Google Scholar
• Ogasawara , H. ( 2006 ). Asymptotic expansion of the sample correlation coefficient under nonnormality . Computat. Statist. Data Anal. 50 : 891 – 910 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Pitman , E. J. G. ( 1937 ). Significance tests which may be applied to samples from any populations. II. The correlation coefficient test . Supplement to the J. Roy. Statist. Soc . 4 : 225 – 232 . [CSA]
   Google Scholar
• Sampson , A. R. ( 1974 ). A tale of two regressions . J. Amer. Statist. Assoc. 69 : 682 – 689 . [CSA]
   Web of Science ®Google Scholar
• Steiger , J. H. , Hakstian , A. R. ( 1982 ). The asymptotic distribution of elements of a correlation matrix: theory and application . Brit. J. Mathemat. Statist. Psychol. 35 : 208 – 215 . [CSA]
   Web of Science ®Google Scholar
• Stuart , A. , Ord , J. K. ( 1994 ). Kendall's Advanced Theory of Statistics: Distribution Theory , 6th ed. . Vol. 1. London : Arnold .
   Google Scholar