Robust estimation and inference in categorical data

Oregon Convention Center 

While many methods exist for robust estimation of models for continuous variables, the literature on robust estimation in categorical data is scarce, although many relevant variables are categorical, such as questionnaire responses, self-reported health, or counting processes. I propose a general framework for robustly estimating statistical functionals or parameters in models for possibly multivariate categorical data. The proposed estimator generalizes maximum likelihood estimation, is strongly consistent, asymptotically Gaussian, and is of the same time complexity as maximum likelihood. In addition, I develop a novel test that tests whether a given observation can be fitted well by the assumed model, thereby conceptualizing the notion of an outlier in categorical data. I verify the attractive statistical properties of the proposed methodology in simulation studies, and demonstrate its practical usefulness in an empirical application on structural equation modeling of questionnaire responses, where I find compelling evidence for the presence of inattentive respondents whose adverse effects the proposed estimator can withstand, unlike maximum likelihood.

Robust statistics

Discrete variables

Multivariate statistics

Asymptotic normality

Outlier detection 

IMS