Valid Inference Corrected for Outlier Removal
This solves the problem of ensuring valid statistical inference for researchers and practitioners in fields like data analysis and econometrics after outlier removal, representing an incremental improvement by applying existing selective inference tools to a specific issue.
The paper addresses the problem of invalid inference in linear regression after outlier removal, showing that the standard 'detect-and-forget' approach leads to incorrect confidence intervals and p-values, and it provides a method using selective inference to correct this, with simulations and real data applications demonstrating differences from traditional strategies.
Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. This standard "detect-and-forget" approach has been shown to be problematic, and in this paper we highlight the fact that it can lead to invalid inference and show how recently developed tools in selective inference can be used to properly account for outlier detection and removal. Our inferential procedures apply to a general class of outlier removal procedures that includes several of the most commonly used approaches. We conduct simulations to corroborate the theoretical results, and we apply our method to three real data sets to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.