David T. Frazier, Ruben Loaiza-Maya, Didier Nibbering
arXiv 14 Aug 2026 · Econometrics
arXiv:2608.13851 · PDF · Extracted main text
Limited dependent variable models are central to empirical economics, but likelihood-based inference is infeasible when likelihoods involve high-dimensional integration over latent variables. This paper proposes Stochastically Estimated Gradient Ascent (SEGA), a scalable estimation approach for limited dependent variable models. Using Fisher's identity, SEGA replaces the intractable likelihood score with an unbiased augmented-data score evaluated at a single conditional draw of the latent variables, and embeds this score in a stochastic gradient ascent algorithm. With sufficiently many iterations, we show that SEGA is asymptotically equivalent to the infeasible maximum likelihood estimator. A variance estimator based on Fisher's and Louis' identities is proposed that allows inference to proceed in the usual manner. Applications to brand choice and household demand demonstrate the usefulness of SEGA for conducting inference in large-scale discrete-choice and censored-demand models.
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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 | Botev, Z. I (2017) The normal law under linear restrictions: simulation and estimation via minimax tilting | 0.843 | 5 | 3 | 60% |
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| 3 | Chen, X., Lee, J. D., Tong, X. T., and Zhang, Y (2020) Statistical inference for model parameters in stochastic gradient descent | 0.737 | 5 | 4 | 40% |
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| 8 | Danaher, P. J., Danaher, T. S., Smith, M. S., and Loaiza-Maya, R (2020) Advertising effectiveness for multiple retailer-brands in a multimedia and multichannel environment self | 0.644 | 2 | 2 | 100% |
| 9 | Louis, T. A (1982) Finding the observed information matrix when using the EM algorithm | 0.644 | 2 | 2 | 100% |
| 10 | Moulines, E. and Bach, F (2011) Non-asymptotic analysis of stochastic approximation algorithms for machine learning | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.