Exact Computation of Maximum Rank Correlation Estimator

TL;DR

This paper introduces a mixed integer programming algorithm for exact computation of the maximum rank correlation estimator, enabling global solutions and improved predictive performance analysis.

Contribution

It develops a novel MIP-based method transforming indicator functions into binary variables for exact estimation, applicable to rank prediction problems.

Findings

Algorithm successfully computes global solutions

Reformulation as MIP enhances computational efficiency

Non-asymptotic bounds improve understanding of predictive performance

Abstract

In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all indicator functions into binary parameters to be estimated and show that it is equivalent to the original problem. We also consider an application of the best subset rank prediction and show that the original optimization problem can be reformulated as MIP. We derive the non-asymptotic bound for the tail probability of the predictive performance measure. We investigate the performance of the MIP algorithm by an empirical example and Monte Carlo simulations.