Robust functional principal components: A projection-pursuit approach

Bali, Juan Lucas; Boente, Graciela; Tyler, David E.; Wang, Jane-Ling

doi:10.1214/11-aos923

Cited by 84 publications

(79 citation statements)

References 29 publications

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“…Neither functional principal components derived from the covariance operator nor least-squares regression methods are robust to anomalous observations and this remains true even if penalized estimators are used. To obtain a robust method we instead propose combining M-estimators of location for functional data, (Sinova et al, 2018), functional principal components based on projection pursuit, (Bali et al, 2011), and MM estimators for regression (Yohai, 1987). We briefly review these ideas and explain their place in our proposal.…”

Section: A Robust Functional Principal Component Estimatormentioning

confidence: 99%

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Robust functional regression based on principal components

Kalogridis

Aelst

2019

Journal of Multivariate Analysis

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Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and therefore are sensitive to atypical observations. To remedy this, we propose a two-step estimation procedure that combines robust functional principal components and robust linear regression. Moreover, we propose a transformation that reduces the curvature of the estimators and can be advantageous in many settings. For these estimators we prove Fisher-consistency at elliptical distributions and consistency under mild regularity conditions. The influence function of the estimators is investigated as well. Simulation experiments show that the proposed estimators have reasonable efficiency, protect against outlying observations, produce smooth estimates and perform well in comparison to existing approaches.

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Section: A Robust Functional Principal Component Estimatormentioning

confidence: 99%

“…Since it is well-known that the sample variance is heavily influenced by outlying observations, Bali et al (2011) proposed using a robust scale functional as the objective function. There are several candidates for the robust scale, but we opt for the Qn estimator (Rousseeuw and Croux, 1993).…”

Section: A Robust Functional Principal Component Estimatormentioning

confidence: 99%

Robust functional regression based on principal components

Kalogridis

Aelst

2019

Journal of Multivariate Analysis

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“…Thus in general, the eigenvalues of the SSCM are less separated than those of V 0 , which is one reason why the use of the SSCM for robust principal component analysis has been questioned (e.g. Bali, Boente, Tyler, and Wang 2011;Magyar and Tyler 2014). However, the differences appear to be generally small in higher dimensions.…”

Section: Eigenvalues Of S(x)mentioning

confidence: 99%

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Dürre

Fried

Vogel

2017

AJS

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We summarize properties of the spatial sign covariance matrix and especially consider the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix. A small simulation study indicates that the new estimator is very efficient under various elliptical distributions if the dimension is large. We furthermore derive its influence function under certain conditions which indicates that the multivariate spatial sign correlation becomes more sensitive to outliers as the dimension increases.

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“…The fPCR method was first proposed by Reiss and Ogden , but they fail to account for the phase variability found in functional data. Additionally, one could use a robust fPCA method such as Bali et al , but this method also fails to account for phase and amplitude variability explicitly in the data. We then extend this framework to the logistic regression case where the response can take on categorical data.…”

Section: Introductionmentioning

confidence: 99%

Elastic functional principal component regression

Tucker

Lewis

Srivastava

2018

Statistical Analysis

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We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phase variability, or handle it via preprocessing, that is, use an off‐the‐shelf technique for functional alignment and phase removal. We develop a functional principal component regression model which has a comprehensive approach in handling phase and amplitude variability. The model utilizes a mathematical representation of the data known as the square‐root slope function. These functions preserve the double-struckL2 norm under warping and are ideally suited for simultaneous estimation of regression and warping parameters. Using both simulated and real‐world data sets, we demonstrate our approach and evaluate its prediction performance relative to current models. In addition, we propose an extension to functional logistic and multinomial logistic regression.

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Robust functional principal components: A projection-pursuit approach

Cited by 84 publications

References 29 publications

Robust functional regression based on principal components

Robust functional regression based on principal components

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Elastic functional principal component regression

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