Abstract: A practical challenge in structural estimation is the requirement to minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions without performing an exhaustive search. It augments each iteration from a new Gauss-Newton algorithm with a grid search step. A finite sample analysis derives its optimization and statistical properties simultaneously under standard econometric assumptions. After a finite number of iterations, the algorithm transitions from global to fast local convergence, producing accurate estimates with high-probability. Simulated examples and an empirical application illustrate the properties and performance of the algorithm. Comparisons with commonly used optimizers and quasi-Bayesian estimation using MCMC are also given.
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