SAUSS: Stochastic Approximation with Unbiased Simulated Scores for Limited Dependent Variable Models

Abstract:Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose Stochastic Approximation with Unbiased Simulated Scores (SAUSS), an averaged stochastic approximation based on conditionally unbiased mini-batch score estimates. Each iteration uses a fixed mini-batch regardless of sample size. For multinomial probit, accept-reject sampling provides exact conditional draws and unbiased score estimates for any fixed number of accepted draws. Under local conditions, asymptotic theory for the averaged estimator and the partial-sum process of the SAUSS iterates incorporates mini-batch and simulation variability and supports random-scaling and plug-in inference. In simulations and an application, SAUSS gives comparable results in less than 1% of the computation time of simulated maximum likelihood. SAUSS extends to limited dependent variable models with conditional-expectation score representations and exact conditional sampling.

Methodology (stat.ME); Machine Learning (cs.LG); Econometrics (econ.EM)

arXiv:2608.25304 [stat.ME]

(or arXiv:2608.25304v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2608.25304 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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