Asymptotic properties of Impulse Indicator Saturation under outlier contamination

Music City Center 

Impulse Indicator Saturation (IIS) is an outlier robust algorithm for estimating linear regression models. It begins by splitting a sample into two halves. Initial least squares estimators from each half are used to classify observations into "good" observations and "outliers", depending on whether their residuals exceed a predetermined cut-off. The IIS estimator is then equal to the least squares estimator on the retained set of `good' observations. I study asymptotic properties of IIS in data generating processes that include outliers. My approach departs from existing literature, where IIS has only been studied without contamination. I write down an asymptotic representation of IIS in terms of an infeasible least squares estimator that perfectly removes all outliers. As a consequence, asymptotic inference with IIS can proceed along the lines of standard least squares theory, and the distributions of test statistics are free of nuisance parameters. I further analyse the False Outlier Discovery Rate (FODR) of IIS, and find a Poisson approximation to its distribution. Simulations and an empirical illustration using macroeconomic time series data are provided.

Outlier detection

Robust estimation and inference

Linear models and regression

Time series 

Business and Economic Statistics Section