Tabu Search for Maximum Score Estimator Computation

A new tabu search algorithm is proposed for the maximum score estimator computation, where the focus is on large sample size and/or large number of parameters. The proposed algorithm shares the same solution representation with the Hyperplanes Intersection Simulated Annealing (HISA) previously published, but also is different to this in several significant aspects. First, it is a deterministic algorithm rather than a stochastic algorithm. Thus, it can be seen as a Tabu Search (TS) generalization of the simpler Hyperplanes Intersection Local Search (HILS). Second, the Tabu Search algorithm is much faster than the Simulated Annealing one, while providing solutions of about the same quality, in terms of objective function attainment and statistical properties of the estimator. Also, this algorithm's performance doesn't depend on the nature of a random number generator as HISA does, and for this reason it is more platform and compiler independent. Source code in Fortran is provided and also a translation to C++ is highlighted. The new approach is tested on a Monte Carlo simulation and three empirical applications. Results show that the TS algorithm is a useful alternative to HISA and can also be combined with it, first quickly running the TS and then providing its partially converged solution to HISA for polishing. Comparison with Mixed Integer Programming (MIP) and Threshold Accepting is also discussed in the paper