发表机构
Columbia University; University of Iowa; The Hong Kong University of Science and Technology; McMaster University（哥伦比亚大学; 爱荷华大学; 香港科技大学; 麦克马斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有限因变量模型，提出SAUSS方法，基于条件无偏小批量得分估计实现高效计算，仅需模拟极大似然1%的时间即可取得相当结果，支持扩展至相关模型。
AI 中文摘要
多项选择模型可提供灵活的替代模式，但当存在大量备选选项或观测值时，其计算需求会显著提升。在固定的单观测模拟预算下，模拟极大似然会引入模拟偏差，且每一步优化都需要对全样本似然进行评估。我们提出带无偏模拟得分的随机近似方法（SAUSS），这是一种基于条件无偏小批量得分估计的平均随机近似方法。每一轮迭代均使用固定大小的小批量样本，与样本规模无关。对于多项probit模型，接受-拒绝采样可提供精确的条件抽样，且对于任意固定数量的接受抽样，均可得到无偏得分估计。在局部条件下，针对平均估计量和SAUSS迭代的部分和过程的渐近理论，纳入了小批量与模拟的变异性，并支持随机缩放和插件推断。在模拟与实际应用中，SAUSS的计算时间不足模拟极大似然的1%，却能给出相当的结果。SAUSS可扩展至具有条件期望得分表示和精确条件抽样的有限因变量模型。
英文摘要
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.
