# Robust Estimation and Inference with Categorical Data

arXiv: https://arxiv.org/abs/2403.11954 · HTML: https://mlsanity.com/paper/2403.11954/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2024.

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

- [Towards Reliable Recommender Systems for Rating Data](https://mlsanity.com/paper/2412.20802/) (2024)

## Abstract (arXiv)

Categorical data pose a distinctive robustness challenge: contingency-table cells need not have a meaningful magnitude, ordering, or metric, so departures must instead be assessed through discrepancies between observed cell frequencies and model-implied probabilities. We develop C-estimation, a unifying framework for robust estimation in structured categorical models. C-estimation limits the influence of large frequency discrepancies and can be applied to unconditional, composite, and regression models of categorical data. Building on minimum-disparity estimation, the framework also accommodates clipped nonsmooth loss functions. A common asymptotic theory establishes Fisher consistency, consistency for the population target and asymptotic normality under contamination, and sandwich covariance estimation. At a correctly specified model, regular C-estimators retain the first-order efficiency of maximum likelihood. To quantify global robustness, we derive computable lower and upper envelopes for maximum-bias curves and, for a Huber-like loss, connect its clipping constants to a global robustness bound. Simulations support the theory and illustrate the estimators' robustness. An application to questionnaire data illustrates robust estimation of a latent factor model and identifies misfitting response strings that may reflect careless responding. A software implementation is provided.