A note on iterative marginal optimization: a simple algorithm for maximum rank correlation estimation

The maximum rank correlation (MRC) estimator was originally studied by Han [1987. Nonparametric analysis of a generalized regression model. J. Econometrics 35, 303–316] and Sherman [1993. The limiting distribution of the maximum rank correlation estimator. Econometrica 61, 123–137] from the econometrics point of view, and most recently attracted much attention from the classification literature due to its close relationship with the receiver operating characteristics (ROC) curve [Baker, 2003. The central role of receiver operating characteristics (ROC) curves in evaluating tests for the early detection of cancer. J. Nat. Cancer Inst. 95, 511–515; Pepe, 2003. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press, Oxford; Pepe et al., 2004. Combining predictors for classification using the area under the ROC curve. University of Washington Biostatistics Working Paper Series]. Compared with its nice theoretical properties and successful applications, the MRC estimator's computational aspects are not trivial. This is because the MRC objective function is neither smooth nor continuous. Therefore, the traditional Newton–Raphson type algorithm cannot be used to find the MRC estimator. As an easy solution, we propose in this article a very simple fitting algorithm named iterative marginal optimization (IMO), which guarantees a monotone increasing of the MRC objective function at each iteration step in a very efficient manner. We show via extensive simulation that the proposed IMO algorithm is not only computationally stable but also reasonably fast. Moreover, real data about the China stock market are analyzed to further illustrate the usefulness of the proposed.