The main contributions of robust statistics to statistical science and a new challenge

Ronchetti, Elvezio

doi:10.1007/s40300-020-00185-3

Cited by 19 publications

(11 citation statements)

References 50 publications

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“…On the other hand, it would also be important to explore whether the circular coordinates with generalized penalty can be helpful in model selection. In dimension reduction, sparsity can be studied further with a view of robust statistics using a geometric induced loss function [39,27]. This line of research is motivated by the statistical literature on generalized penalty functions [19].…”

Section: Discussionmentioning

confidence: 99%

Generalized penalty for circular coordinate representation

Luo¹,

Patania²,

Kim³

et al. 2021

FoDS

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<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. To do that, we use a generalized penalty function instead of an <inline-formula><tex-math id="M1">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analyses to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.</p>

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Section: Discussionmentioning

confidence: 99%

Generalized penalty for circular coordinate representation

Luo¹,

Patania²,

Kim³

et al. 2021

FoDS

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“…Hence, (72) can be viewed as fitting a nonlinear regression on covariances using a particular robust loss function ρ [40]. Again, the function H defines an M-estimation problem [29,31], and its use is justified by the hope that model errors s ij − σ ij (γ) are treated as outliers by utilizing the robust loss function ρ [19,47]. Hence, the model errors should not impact the estimate of the parameter vector γ.…”

Section: Robust Moment Estimation (Rme)mentioning

confidence: 99%

“…There is literature investigating the robustness of SEM estimation to non-normal distributions [13][14][15]. This kind of robustness that relies on contaminated distributions [16][17][18][19] is not the target of this article. Instead, we rely on the concept of model robustness; that is, how robust is an SEM estimation method in the presence of local model misspecifications.…”

Section: Introductionmentioning

confidence: 99%

Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches

Robitzsch

2022

Stats

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Structural equation models (SEM), or confirmatory factor analysis as a special case, contain model parameters at the measurement part and the structural part. In most social-science SEM applications, all parameters are simultaneously estimated in a one-step approach (e.g., with maximum likelihood estimation). In a recent article, Rosseel and Loh (2022, Psychol. Methods) proposed a two-step structural after measurement (SAM) approach to SEM that estimates the parameters of the measurement model in the first step and the parameters of the structural model in the second step. Rosseel and Loh claimed that SAM is more robust to local model misspecifications (i.e., cross loadings and residual correlations) than one-step maximum likelihood estimation. In this article, it is demonstrated with analytical derivations and simulation studies that SAM is generally not more robust to misspecifications than one-step estimation approaches. Alternative estimation methods are proposed that provide more robustness to misspecifications. SAM suffers from finite-sample bias that depends on the size of factor reliability and factor correlations. A bootstrap-bias-corrected LSAM estimate provides less biased estimates in finite samples. Nevertheless, we argue in the discussion section that applied researchers should nevertheless adopt SAM because robustness to local misspecifications is an irrelevant property when applying SAM. Parameter estimates in a structural model are of interest because intentionally misspecified SEMs frequently offer clearly interpretable factors. In contrast, SEMs with some empirically driven model modifications will result in biased estimates of the structural parameters because the meaning of factors is unintentionally changed.

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“…Here, we assume that the measurement is either observed or missing for all variables and do not consider the case where the measurements for one index are observed for some variables but missing for others. Two main characteristics are observed for the existing clustering methods: first, for imbalanced multivariate functional data, no specific distance measurements are defined and the model-based clustering methods, except for that of Misumi et al (2019), cannot be applied directly; second, the above methods rarely consider outliers, though real data are often corrupted by noises and outliers, see Ronchetti (2021) for a recent review. Although some improvements have been achieved in K-means clustering (Wang & Su 2011) and hierarchical clustering (Gagolewski et al 2016) for multivariate data to reduce the influence of outliers, robust (i.e., outlier-resistant) clustering algorithms for sparse multivariate functional data are lacking.…”

Section: Introductionmentioning

confidence: 99%

Robust Two-Layer Partition Clustering of Sparse Multivariate Functional Data

Qu¹,

Dai²,

Genton³

2022

Preprint

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In this work, a novel elastic time distance for sparse multivariate functional data is proposed. This concept serves as the foundation for clustering functional data with various time measurements per subject. Subsequently, a robust two-layer partition clustering is introduced. With the proposed distance, our approach not only is applicable to both complete and imbalanced multivariate functional data but also is resistant to outliers and capable of detecting outliers that do not belong to any clusters. The classical distance-based clustering methods such as K-medoids and agglomerative hierarchical clustering are extended to the sparse multivariate functional case based on our proposed distance. Numerical experiments on the simulated data highlight that the performance of the proposed algorithm is superior to the performances of the existing modelbased and extended distance-based methods. Using Northwest Pacific cyclone track data as an example, we demonstrate the effectiveness of the proposed approach. The code is available online for readers to apply our clustering method and replicate our analyses.

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The main contributions of robust statistics to statistical science and a new challenge

Cited by 19 publications

References 50 publications

Generalized penalty for circular coordinate representation

Generalized penalty for circular coordinate representation

Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches

Robust Two-Layer Partition Clustering of Sparse Multivariate Functional Data

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