Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

Barrios, Erniel B.

doi:10.5351/csam.2015.22.6.543

CSAM

2015

DOI: 10.5351/csam.2015.22.6.543

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Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

Erniel B. Barrios

Abstract: We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, non… Show more

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Cited by 2 publications

References 65 publications

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Robust gradient boosting for generalized additive models for location, scale and shape

Speller,

Staerk,

Gude

et al. 2023

Adv Data Anal Classif

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Due to the increasing complexity and dimensionality of data sources, it is favorable that methodological approaches yield robust results so that corrupted observations do not jeopardize overall conclusions. We propose a modelling approach which is robust towards outliers in the response variable for generalized additive models for location, scale and shape (GAMLSS). We extend a recently proposed robustification of the log-likelihood to gradient boosting for GAMLSS, which is based on trimming low log-likelihood values via a log-logistic function to a boundary depending on a robustness constant. We recommend a data-driven choice for the involved robustness constant based on a quantile of the unconditioned response variable and investigate the choice in a simulation study for low- and high-dimensional data situations. The versatile application possibilities of robust gradient boosting for GAMLSS are illustrated via three biomedical examples—including the modelling of thyroid hormone levels, spatial effects for functional magnetic resonance brain imaging and a high-dimensional application with gene expression levels for cancer cell lines.

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Robust gradient boosting for generalized additive models for location, scale and shape

Speller,

Staerk,

Gude

et al. 2023

Adv Data Anal Classif

View full text Add to dashboard Cite

show abstract

Robust statistical boosting with quantile-based adaptive loss functions

Speller

Staerk

Mayr

2022

The International Journal of Biostatistics

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We combine robust loss functions with statistical boosting algorithms in an adaptive way to perform variable selection and predictive modelling for potentially high-dimensional biomedical data. To achieve robustness against outliers in the outcome variable (vertical outliers), we consider different composite robust loss functions together with base-learners for linear regression. For composite loss functions, such as the Huber loss and the Bisquare loss, a threshold parameter has to be specified that controls the robustness. In the context of boosting algorithms, we propose an approach that adapts the threshold parameter of composite robust losses in each iteration to the current sizes of residuals, based on a fixed quantile level. We compared the performance of our approach to classical M-regression, boosting with standard loss functions or the lasso regarding prediction accuracy and variable selection in different simulated settings: the adaptive Huber and Bisquare losses led to a better performance when the outcome contained outliers or was affected by specific types of corruption. For non-corrupted data, our approach yielded a similar performance to boosting with the efficient L 2 loss or the lasso. Also in the analysis of skewed KRT19 protein expression data based on gene expression measurements from human cancer cell lines (NCI-60 cell line panel), boosting with the new adaptive loss functions performed favourably compared to standard loss functions or competing robust approaches regarding prediction accuracy and resulted in very sparse models.

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Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

Cited by 2 publications

References 65 publications

Robust gradient boosting for generalized additive models for location, scale and shape

Robust gradient boosting for generalized additive models for location, scale and shape

Robust statistical boosting with quantile-based adaptive loss functions

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