2023/02/13 by Roberto Imbuzeiro Moraes Felinto de Oliveira, Oliveira, Roberto I., Lucas H. G. Resende +1 · 1 citation
Mathematics · #62G35 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #Survey Sampling and Estimation Techniques
paper · pdf · doi:10.48550/arxiv.2302.06710
openalex publication_date 2023/02/13 · openalex created_date 2023/02/17 · openalex updated_date 2026/07/28
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating expectations of functions in a given family, with uniform error bounds; this is closely related to the problem of estimating the mean of a random vector under a general norm. The second problem considered is that of regression with quadratic loss. In both cases, trimmed-mean-based estimators are the first to obtain optimal dependence on the (adversarial) contamination level. Moreover, they also match or improve upon the state of the art in terms of heavy tails. Experiments with synthetic data show that a natural ``trimmed mean linear regression'' method often performs better than both ordinary least squares and alternative methods based on median-of-means.