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Inference concerning the population correlation coefficient from bivariate normal samples based on minimal observations

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Summary

Let (X, Y) be bivariate normally distributed with means (μ 1,μ 2), variances (σ 21 ,σ 22 ) and correlation betweenX andY equal to ρ. Let (X i ,Y i ) be independent observations on (X,Y) fori=1,2,...,n. Because of practical considerations onlyZ i =min (X i ,Y i) is observed. In this paper, as in certain routine applications, assuming the means and the variances to be known in advance, an unbiased consistent estimator of the unknown distribution parameter ρ is proposed. A comparison between the traditional maximum likelihood estimator and the unbiased estimator is made. Finally, the problem is extended to multivariate normal populations with common mean, common variance and common non-negative correlation coefficient.

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Authors and Affiliations

  1. University of Queensland, Queensland, Australia

    G. Baikunth Nath

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  1. G. Baikunth Nath
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Baikunth Nath, G. Inference concerning the population correlation coefficient from bivariate normal samples based on minimal observations. Ann Inst Stat Math 29, 259–273 (1977). https://doi.org/10.1007/BF02532788

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  • DOI: https://doi.org/10.1007/BF02532788

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