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Inferences on correlation coefficients: One-sample,independent and correlated cases
Authors:K Krishnamoorthy  Yanping Xia
Institution:Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
Abstract:This article concerns inference on the correlation coefficients of a multivariate normal distribution. Inferential procedures based on the concepts of generalized variables (GVs) and generalized pp-values are proposed for elements of a correlation matrix. For the simple correlation coefficient, the merits of the generalized confidence limits and other approximate methods are evaluated using a numerical study. The study indicates that the proposed generalized confidence limits are uniformly most accurate even for samples as small as three. The results are extended for comparing two independent correlations, overlapping and non-overlapping dependent correlations. For each problem, the properties of the GV approach and other asymptotic methods are evaluated using Monte Carlo simulation. The GV approach produces satisfactory results for all the problems considered. The methods are illustrated using a few practical examples.
Keywords:Coverage probabilities  Fisher's z transformation  Sizes  UMP test  Uniformly most accurate confidence interval
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