The Collected Works of Wassily Hoeffding pp 57-107 | Cite as
Scale—Invariant Correlation Theory
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Abstract
The problem of correlation may be described as the investigation of those properties of multivariate distributions which characterize these distributions, i.e., do not occur for univariate distributions. These properties depend above all on the relationships of the variables to each other. From the totality of those properties which belong to the topic of correlation one particular class of properties will be considered more closely.
Keywords
Orthogonal Polynomial Functional Dependence Polynomial Expansion Bivariate Distribution Distribution Surface
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Notes
- 3.See a C. Spearman, The Proof and Measurement of Association between Two Things, American Journal of Psychology 15 (1904), pp. 79–82; b) idem, Footrule for Measuring Correlation, British Journal of Psychology 2 (1906), §2.Google Scholar
- 4.See C. Spearman, The Proof and Measurement of Association between Two Things, American Journal of Psychology 15 (1904), pp. 79–82 loc. cit. 3b, §2.Google Scholar
- 8.[ntObviously without knowledge of Lindeberg’s work, M. G. Kendall in A New Measure of Rank Correlation, Biometrika 30 (1938), pp. 81–93, proposed a measure of correlation which agrees in essence with the correlation percent.MathSciNetzbMATHGoogle Scholar
- 10.H. Hotelling and. M. R. Pabst, Rank Correlation and Tests of Significance Involving No Assumption of Normality, Annals of Mathematical Statistics 7 (1936), pp. 29–43.CrossRefGoogle Scholar
- 11.loc. cit. 10, pp. 30–31.Google Scholar
- 15.See the “correlation function of strip type” of K. G. Hagström, Bemerkungen zur Theorie der statistischen Funktionen, Skandinavisk Aktuarietidskrift 2 (1919), pp. 204–205.Google Scholar
- 16.See K. Pearson, Bemerkungen zur Theorie der statistischen Funktionen, Skandinavisk Aktuarietidskrift 2 (1919) loc. cit. 9, § 4Google Scholar
- 17.See, e.g., H. Cramer, Remarks on Correlation, Skandinavisk Aktuarietidskrift 7 (1924), pp 230–231, and R. v. Mises, loc. cit. 5b, p. 359; see here also on pp. 315-316 the remarks concerning X 2.Google Scholar
- 18.loc. cit. 5a, p. 16.Google Scholar
- 19.K. Pearson, Remarks on Correlation, Skandinavisk Aktuarietidskrift 7 (1924) loc. cit. 9, p. 12.Google Scholar
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© Springer Science+Business Media New York 1994