Exponential probability inequality and convergence results for the median absolute deviation and its modifications

DOI10.1016/j.spl.2009.05.001zbMath1456.62056OpenAlexW2054392873MaRDI QIDQ840789

Robert J. Serfling, Satyaki Mazumder

Publication date: 14 September 2009

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2009.05.001

zbMATH Keywords

median absolute deviation from the median (MAD)

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items (10)

Bahadur representations for the median absolute deviation and its modifications ⋮ The exact finite-sample distribution of the median absolute deviation about the median of continuous random variables ⋮ Estimating velocity for processive motor proteins with random detachment ⋮ Stabilized hard thresholding for an unknown noise level ⋮ On masking and swamping robustness of leading nonparametric outlier identifiers for multivariate data ⋮ High-dimensional robust precision matrix estimation: cellwise corruption under \(\epsilon \)-contamination ⋮ Sklar's Omega: A Gaussian Copula-Based Framework for Assessing Agreement ⋮ Scale calibration for high-dimensional robust regression ⋮ Optimally robust estimators in generalized Pareto models ⋮ Robust scale estimation under shifts in the mean

Cites Work

• Limit theorems for the median deviation
• Bahadur representations for robust scale estimators based on regression residuals
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Finite sample breakdown points of projection based multivariate location and scatter statistics
• Asymptotic independence of median and MAD
• A note on Tyler's modification of the MAD for the Stahel-Donoho estimator
• On MAD and comedians
• Projection-based depth functions and associated medians
• Multiple outlier detection in multivariate data using projection pursuit techniques
• Another approach to asymptotics and bootstrap of randomly trimmed means
• Approximation Theorems of Mathematical Statistics
• The Breakdown Points of the Mean Combined with Some Rejection Rules
• Asymptotically Optimal Tests for Multinomial Distributions
• A New Proof of the Bahadur Representation of Quantiles and an Application
• Complete Convergence and the Law of Large Numbers
• High breakdown analogs of the trimmed mean

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