🤖 AI Summary
In structural estimation, objective functions are often noisy, nonsmooth, and nonconvex, causing conventional optimization methods to readily converge to local minima and hindering rigorous characterization of statistical properties. To address this, we propose a hybrid algorithm integrating an enhanced Gauss–Newton method with adaptive grid search: grid search ensures robust global exploration in early stages, followed by a seamless transition to the improved Gauss–Newton method for rapid local convergence. For the first time under purely econometric assumptions—without restrictive smoothness or convexity conditions—we simultaneously establish finite-sample optimization error bounds and the asymptotic distribution of the estimator. Simulation studies and empirical applications demonstrate that our method substantially improves estimation accuracy and convergence stability, attaining the true solution with high probability while avoiding exhaustive search. It thus achieves an optimal trade-off between computational efficiency and statistical reliability.
📝 Abstract
A practical challenge for structural estimation is the requirement to accurately 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 using only econometric assumptions. After a finite number of iterations, the algorithm automatically transitions from global to fast local convergence, producing accurate estimates with high probability. Simulated examples and an empirical application illustrate the results.