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Smith, Murray D. and Moffatt, P. G. (1998): Fisher's Information on the Correlation Coefficient in Bivariate Models. Collaborative Research Center 386, Discussion Paper 126
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Abstract

From a theoretical perspective, we consider the properties of the maximum likelihood estimator of the correlation coefficient, principally regarding precision, in various types of bivariate model which are popular in the applied literature. The models are: "Full-Full", in which both variables are fully observed; "Censored-Censored", in which both of the variables are censored at zero; and finally, "Binary-Binary", in which both variables are observed only in sign. For analytical convenience, the underlying bivariate distribution which we assume in each of these cases is the bivariate logistic. A central issue is the extent to which censoring reduces the level of Fisher's Information pertaining to the correlation coefficient, and therefore reduces the precision with which this important parameter can be estimated.