Inference concerning the population correlation coefficient from bivariate normal samples based on minimal observations
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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.
KeywordsCommon Variance Maximum Likelihood Estimator Unbiased Estimator Moment Generate Function Case R162
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