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The best lower bound of sample correlation coefficient with ordered restriction

Author

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  • Hwang, Tea-Yuan
  • Hu, Chin-Yuan

Abstract

In this paper, it is shown that the sample correlation coefficient between two sets of ordered samples x(1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] x(n) and y(1) [less-than-or-equals, slant] ... [less-than-or-equals, slant] y(n) is greater than or equal to 1/(n-1); and the best lower bound can be attained if and only if one of the following holds: (a) x(1)

Suggested Citation

  • Hwang, Tea-Yuan & Hu, Chin-Yuan, 1994. "The best lower bound of sample correlation coefficient with ordered restriction," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 195-198, February.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:3:p:195-198
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    Cited by:

    1. Giovanni Giorgi, 2015. "Remembering Carlo Benedetti," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 299-301, December.
    2. Giovanni Maria Giorgi, 2005. "Encounter with the Italian Statistical School: A conversation with Carlo Benedetti," Econometrics 0507009, University Library of Munich, Germany.
    3. Chin-Yuan Hu & Gwo Dong Lin, 2022. "Characterizations of the normal distribution via the independence of the sample mean and the feasible definite statistics with ordered arguments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 473-488, June.

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    Keywords

    62H20 Correlation coefficient;

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