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On estimating a transformation correlation coefficient

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  • Kelly Zou
  • W. J. Hall

Abstract

We consider a semiparametric and a parametric transformation-to-normality model for bivariate data. After an unstructured or structured monotone transformation of the measurement scales, the measurements are assumed to have a bivariate normal distribution with correlation coefficient „ , here termed the 'transformation correlation coefficient'. Under the semiparametric model with unstructured transformation, the principle of invariance leads to basing inference on the marginal ranks. The resulting rank-based likelihood function of „ is maximized via a Monte Carlo procedure. Under the parametric model, we consider Box-Cox type transformations and maximize the likelihood of „ along with the nuisance parameters. Efficiencies of competing methods are reported, both theoretically and by simulations. The methods are illustrated on a real-data example.

Suggested Citation

  • Kelly Zou & W. J. Hall, 2002. "On estimating a transformation correlation coefficient," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 745-760.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:745-760
    DOI: 10.1080/02664760120098801
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    1. Kelly Zou & W. J. Hall, 2002. "Semiparametric and parametric transformation models for comparing diagnostic markers with paired design," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(6), pages 803-816.
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