Robust estimation and inference with categorical data

02.10.2026 11:15 – 12:15

RESEARCH INSTITUTE FOR STATISTICS AND INFORMATION SCIENCE SEMINARS

ABSTRACT

Categorical data---including questionnaire responses, network measurements, and event counts---are central to empirical research in the social, health, and economic sciences. Yet, such data may contain atypical or corrupted observations arising, for example, from careless or bot responses, sampling errors, or measurement errors. Even limited contamination can distort estimates and inference by making a postulated model poorly suited to observed data. Robust estimation is especially challenging in this setting because contingency-table cells need not possess a meaningful magnitude, ordering, or metric. Model departures must therefore 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-estimators limit the influence of cells whose observed frequencies disagree with their fitted probabilities. The framework is very general and covers unconditional, composite, and regression models. Building on minimum-disparity estimation, it also accommodates clipped nonsmooth Huber-type loss functions. We establish Fisher consistency, consistency for the population target, asymptotic normality under contamination, and sandwich covariance estimation. When the model is correctly specified, 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 theoretical results and illustrate the estimators' robustness. An application to psychological questionnaire data demonstrates robust estimation of a latent factor model and flags response strings that are poorly represented by the model, some of which may reflect careless responding. A software implementation is provided in the R package "robcat", which is freely available from the CRAN.

Link to arXiv-preprint: https://arxiv.org/abs/2403.11954

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