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

  • G. Baikunth Nath
Article

Summary

Let (X, Y) be bivariate normally distributed with means (μ 1,μ 2), variances (σ 1 2 ,σ 2 2 ) 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.

Keywords

Common Variance Maximum Likelihood Estimator Unbiased Estimator Moment Generate Function Case R162 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Institute of Statistical Mathematics 1977

Authors and Affiliations

  • G. Baikunth Nath
    • 1
  1. 1.University of QueenslandAustralia

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