Description

Robust statistics is a branch of statistics that focuses on methods that are resistant to outliers or other departures from standard assumptions. Traditional statistical methods can be sensitive to outliers, leading to biased estimates or misleading inferences. Robust methods aim to provide reliable statistical analysis even when data deviates from the standard assumptions.

For example, robust estimators like the median and trimmed mean are less influenced by outliers compared to the mean. Measures like the Median Absolute Deviation offer robust alternatives to traditional dispersion measures like standard deviation. Robust regression techniques like Huber regression and least absolute deviation regression mitigate the impact of outliers in regression analysis. Nonparametric methods also play a vital role, offering distribution-free approaches without strict assumptions about the data distribution.

The goal is to explore the principles, applications, and computational aspects of robust statistics and their practical implementation using the statistical software R.

Prerequisites

• Statistical Inference
• Statistical Modelling or Data Science and Statistical Computing
• Familiarity with the statistical software R

References

• Wilcox RR (2021). Introduction to Robust Estimation and Hypothesis Testing. 5th edition. Academic Press. Link
• Huber PJ, Ronchetti E (2009). Robust statistics. 2nd ed. Hoboken, Wiley. Link
• Rousseeuw PJ, Leroy AM (2003). Robust regression and outlier detection. Hoboken, Wiley-Interscience. Link
• AMC (2001). Robust statistics: a method of coping with outliers. Link
• Rousseeuw, PJ, Hubert, M. (2018), Anomaly detection by robust statistics. WIREs Data Mining Knowl Discov, 8: e1236. Link