Essays on outlier robustness

Thesis

This thesis studies outlier robust statistical methods under contamination, motivated by empirical challenges in economics.

Chapter 1 examines the robustness of the Least Trimmed Squares estimator in linear models with categorical covariates. We find uniform boundedness guarantees that apply to a chosen sub-coefficient of interest. We show that LTS is robust in a wider range of settings than suggested by existing boundedness and breakdown point results. We also propose a data-driven approach to choosing an initial LTS tuning parameter, which is useful for methods that estimate the number of outliers.

Chapter 2 develops asymptotic theory for the Impulse Indicator Saturation (IIS) method under contamination. We show the asymptotic equivalence of IIS to an infeasible least squares estimator that perfectly removes all outliers. We use this equivalence to derive the distribution of IIS estimators in cross-sectional and time series models with outliers. We further find a limit theory for the number of misclassified ‘clean’ observations.

Chapter 3 decomposes inflation to demand- and supply-driven components in a panel of 32 countries, drawing on the theory of IIS estimators developed in Chapter 2 to guard against outliers around the COVID-19 pandemic. We validate the decomposed inflation series by examining their relationship to external measures of demand and supply shocks. The decompositions are used in applications to post-2020 inflation dynamics and Phillips curves analysis.

Authors: Hao, O

• DOI: 10.5287/ora-5rx46znge
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Subjects: Robust statistics; Econometrics