# SLIM: Stochastic Learning and Inference in Overidentified Models

arXiv: https://arxiv.org/abs/2510.20996 · HTML: https://mlsanity.com/paper/2510.20996/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [SAUSS: Stochastic Approximation with Unbiased Simulated Scores for Limited Dependent Variable Models](https://mlsanity.com/paper/2608.25304/) (2026)

## Abstract (arXiv)

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. Independent mini-batches of moments and derivatives yield unbiased update directions with martingale difference noise. Under suitable regularity conditions, SLIM yields consistent and asymptotically normal estimators without a consistent initial estimator or a globally convex GMM criterion. Our theory covers fixed-sample and random-sampling asymptotics. An optional second-order refinement achieves full-sample GMM efficiency. Random-scaling and plug-in inference account for sampling and computational uncertainty, while debiased J-tests permit specification testing with SLIM. We extend the framework to clustered data with unequal cluster sizes, preserving the form of the inference procedures. Monte Carlo experiments for a nonlinear demand system with 576 moments and 380 parameters demonstrate computational gains and scalability to one million observations. A large-scale LinkedIn application with 4.8 million college graduates illustrates clustered estimation and inference for first employment destinations.