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Correlation is first order independent of transformation

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  • Christopher Withers
  • Saralees Nadarajah

Abstract

We show that the correlation between the estimates of two parameters is almost unchanged if they are each transformed in an arbitrary way. To be more specific, the correlation of two estimates is invariant (except for a possible sign change) up to a first order approximation, to smooth transformations of the estimates. There is a sign change if exactly one of the transformations is decreasing in a neighborhood of its parameter. In addition, we approximate the variance, covariance and correlation between functions of sample means and moments. Copyright Springer-Verlag 2013

Suggested Citation

  • Christopher Withers & Saralees Nadarajah, 2013. "Correlation is first order independent of transformation," Statistical Papers, Springer, vol. 54(2), pages 443-456, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:443-456
    DOI: 10.1007/s00362-012-0442-5
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    References listed on IDEAS

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    1. Radosław Kala & Paweł Pordzik, 2009. "Estimation in singular partitioned, reduced or transformed linear models," Statistical Papers, Springer, vol. 50(3), pages 633-638, June.
    2. Dejian Lai, 2010. "Box–Cox transformation for spatial linear models: a study on lattice data," Statistical Papers, Springer, vol. 51(4), pages 853-864, December.
    3. C. Withers, 1988. "Nonparametric confidence intervals for functions of several distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 727-746, December.
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    More about this item

    Keywords

    Correlation; Covariance; Transformation; Variance; 62E20;
    All these keywords.

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