Analysis of the linear correlation coefficient using pseudo-likelihoods |
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Authors: | F Bertolino W Racugno |
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Institution: | (1) Dip. di Matematica, Università di Cagliari, V. le Merello, 94, 09123 Cagliari, Italy |
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Abstract: | Summary The problem of the inferential analysis of the linear correlation coefficient of normal bivariate populations is tackled,
both from the likelihood and Bayesian viewpoints. In particular it is shown how, using pseudo-likelihood (marginal likelihood
function and profile likelihood), hypotheses such asH
0:ϱ=ϱ0 andH
0:ϱx=ϱy can be verified without prohibitive computation effort. The results of marginal and profile likelihood are compared and it
is shown that these two methods are virtually equivalent even for small sample sizes. Furthermore, in suitable conditions,
the posterior distribution of the coefficient ϱ can be readily obtained, using the exact form or different approximate formulations
of the marginal or profile likelihood. Lastly some possible prior distributions of ϱ are illustrated and some explanatory
examples are presented. |
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Keywords: | linear correlation parameters of interest nuisance parameters pseudolikelihood marginal likelihood profile likelihood residual likelihood asymptotic approximation Bayesian approach |
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