Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin
arXiv 26 Aug 2026 · Statistics — Methodology
arXiv:2608.25304 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hajivassiliou, V. A. and D. L. McFadden (1998) The method of simulated scores for the estimation of LDV models | 1.000 | 5 | 3 | 100% |
| 2 | Train, K. E (2009) Discrete Choice Methods with Simulation\/ (2nd ed.) | 0.928 | 4 | 3 | 100% |
| 3 | Polyak, B. T. and A. B. Juditsky (1992) Acceleration of stochastic approximation by averaging | 0.843 | 4 | 3 | 75% |
| 4 | Börsch-Supan, A. and V. A. Hajivassiliou (1993) Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models | 0.737 | 3 | 2 | 100% |
| 5 | Hajivassiliou, V., D. McFadden, and P. Ruud (1996) Simulation of multivariate normal rectangle probabilities and their derivatives: Theoretical and computational results | 0.737 | 3 | 2 | 100% |
| 6 | Lee, S., Y. Liao, M. H. Seo, and Y. Shin (2022) Fast and robust online inference with stochastic gradient descent via random scaling self | 0.644 | 2 | 2 | 100% |
| 7 | Lee, S., Y. Liao, M. H. Seo, and Y. Shin (2025) Fast inference for quantile regression with tens of millions of observations self | 0.644 | 2 | 2 | 100% |
| 8 | Boneva, T., M. Golin, K. Kaufmann, and C. Rauh (2026) Beliefs about maternal labour supply | 0.511 | 2 | 1 | 100% |
| 9 | Geweke, J., M. P. Keane, and D. E. Runkle (1994) Alternative computational approaches to inference in the multinomial probit model | 0.511 | 2 | 1 | 100% |
| 10 | Albert, J. H. and S. Chib (1993) Bayesian analysis of binary and polychotomous response data | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.