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

2026-08-25

AI Summary

针对多项选择模型计算复杂的问题，提出了一种基于无偏模拟分数的随机逼近方法SAUSS，通过固定迷你批次迭代，大幅减少了计算时间。

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.

Problem

• Multinomial choice models
• simulation bias
• full-sample likelihood evaluation

Innovation

• Stochastic Approximation
• Unbiased Simulated Scores
• Mini-batch
• Conditional Sampling
• Limited Dependent Variable Models