Robust estimation and inference in discrete data

2932 

Contributed Abstract 

Paper 

Max Welz (1)

(1) Erasmus University Rotterdam, Netherlands

Max Welz  
Erasmus University Rotterdam

Max Welz  
N/A

While many methods exist for robust estimation of models for continuous variables, the literature on robust estimation in discrete data is scarce, although many relevant variables are discrete, such as questionnaire responses, self-reported health, or counting processes. I propose a general framework for robustly estimating statistical functionals in models for possibly multivariate discrete 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 an observation can be fitted well by the assumed model, thereby conceptualizing the notion of an outlier in discrete data. I verify the attractive statistical properties of the proposed methodology in simulation studies, and demonstrate its practical usefulness in an empirical application on association estimation in questionnaire responses, where I find evidence for inattentive responding.

Robust statistics|Discrete variables|Multivariate statistics|Asymptotic normality|Outlier detection|

IMS

Statistical Methodology