Robust Estimation and Inference with Categorical Data

Max Welz

Papers from arXiv.org

Abstract: 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.

Date: 2024-03, Revised 2026-09
New Economics Papers: this item is included in nep-ecm and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2403.11954 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2403.11954

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().