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Robust group-Lasso for functional regression model

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2017年第5期46卷 3356-3374页

作者： Pannu, Jasdeep Billor, Nedret Auburn Univ Dept Math & Stat 221 Park Hall Auburn AL 36849 USA

In this article, we consider the problem of selecting functional variables using the L1 regularization in a functional linear regression model with a scalar response and functional predictors, in the presence of outliers. Since the LASSO is a special case of the penalized least-square regression with L1 penalty function, it suffers from the heavy-tailed errors and/or outliers in data. Recently, Least Absolute Deviation (LAD) and the LASSO methods have been combined (the LAD-LASSO regression method) to carry out robust parameter estimation and variable selection simultaneously for a multiple linear regression model. However, variable selection of the functional predictors based on LASSO fails since multiple parameters exist for a functional predictor. Therefore, group LASSO is used for selecting functional predictors since group LASSO selects grouped variables rather than individual variables. In this study, we propose a robust functional predictor selection method, the LAD-group LASSO, for a functional linear regression model with a scalar response and functional predictors. We illustrate the performance of the LAD-group LASSO on both simulated and real data.

关键词： functional regression model LAD-LASSO LASSO Outliers Variable selection Primary 60 Secondary 60

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Robust sparse functional regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2022年第9期51卷 4883-4903页

作者： Pannu, Jasdeep Billor, Nedret Calif State Univ Sacramento Math & Stat Shasta Hall Sacramento CA 95819 USA Auburn Univ Math & Stat Auburn AL 36849 USA

The presence of outliers, in general, affects the performance of the conventional statistical methods which require the homogeneity of observations. In this study, we consider variable selection problem in a functional regression model when a functional dataset contains outliers. We propose a functional adaptive group LASSO variable selection method based on the weighted least absolute deviation which takes into account the effect of outliers in bothxandydirections for a functional regression model with a scalar response and multiple functional predictors. Further, we demonstrate, through simulated and real datasets, that the proposed methods perform well.

关键词： functional outliers functional regression model LASSO Least absolute deviation Robustness Variable selection

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Robust Group Variable Selection Methods for Multiple functional regression model

Robust Group Variable Selection Methods for Multiple Functio...

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作者： Pannu, Jasdeep Auburn University

学位级别：Ph.D., Doctor of Philosophy

With the advancements in science and ever changing technology to collect data, functional data have become common these days, especially in various fields such as neuroscience, chemometrics, e-commerce and computer science. Thus, in last two decades a vast amount of new statistical methodologies to analyze such data, so-called, functional data analysis, have been developed. Much research has been done in various areas of functional data analysis like functional linear regression, functional logistic regression, functional ANOVA, functional principal component analysis and functional outlier detection. Just as in ordinary multiple regression analysis, variable selection is an important problem in the functional regression framework. The area of functional variable selection is seldom discussed in functional data analysis. The classical existing functional variable selection methods are all based on minimizing the penalized residual sum of squares, which is non-robust in nature, in the presence of outliers. In this work, we study robust variable selection methods for functional regression model with a scalar response and functional predictors in the presence of outliers. Essentially, we consider ways that minimize the effect of outliers on the parameter estimator and selector. Since multiple parameters exist for a functional predictor group variable selection methods are used for selecting functional predictors that select grouped variables rather than individual variables. We consider the problem of selecting functional predictors using the L1 regularization in a functional linear regression model with a scalar response and functional predictors in the presence of outliers. Four estimation approaches are discussed: functional LAD- group LASSO, functional Weighted LAD- group LASSO, functional LAD- Adaptive group LASSO and functional Weighted LAD- Adaptive group LASSO. We present an extensive simulation study and a real world example to illustrate the performance of th

关键词： functional regression model LAD-LASSO Outliers Variable selection Robust

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Sure independent screening for functional regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Yuan, Yuan Billor, Nedret Auburn Univ Dept Math & Stat Auburn AL USA Auburn Univ Dept Math & Stat Auburn AL 36830 USA

Due to rapid advancements in computer technology, high-dimensional, big, and complex data, such as functional data, where observations are considered as curves, have emerged from many applications in various disciplines of sciences, such as biomedicine, chemometrics, engineering, and social sciences. Variable selection has consequently become one of the most important problems in statistical research in recent years. As the functional data are inherently infinite dimensional, variable selection problem in multiple functional regression model is, therefore, challenging and difficult. In this study, we extend Sure Independence Screening (SIS) method to a multiple functional regression model with a scalar response and functional predictors. We show that the SIS-based procedure for multiple functional regression model retaining important functional predictors while screening out unimportant functional predictors, and reduce the dimension efficiently. Our methodologies are validated by simulation studies as well as some applications to data.

关键词： functional data analysis functional regression model Sure independence screening Ultra-high dimensionality Variable screening Variable selection

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A fuzzy functional linear regression model with functional predictors and fuzzy responses

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SOFT COMPUTING 2022年第6期26卷 3029-3043页

作者： Hesamian, Gholamreza Akbari, Mohammad Ghasem Payame Noor Univ Dept Stat Tehran 193953697 Iran Univ Birjand Dept Stat Birjand 61597175 Iran

A novel functional regression model was introduced in this research in which, the predictor is a curve linked to a scalar fuzzy response variable. An absolute error-based penalized method with SCAD loss function was also proposed to evaluate the unknown components of the model. For this purpose, a concept of fuzzy-valued function was developed and discussed. Then, a fuzzy large number notion was proposed to estimate the fuzzy-valued function. The performance of the proposed method was examined by some common goodness-of-fit criteria. The efficiency of the proposed method was then evaluated through two numerical examples;a simulation study and an applied example in the scope of watershed management. The proposed method was also compared with several common fuzzy regression models in cases where the functional data were converted to scalar ones.

关键词： Goodness-of-fit measure functional fuzzy number SCAD penalty functional regression model

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regression modelING FOR COMPUTER model VALIDATION WITH functional RESPONSES

REGRESSION MODELING FOR COMPUTER MODEL VALIDATION WITH FUNCT...

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ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference

作者： Liu, Xuyuan Tsui, Kwok-Leung Chen, Wei Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

ISBN: (纸本)9780791843253

Statistical analysis of functional responses based on functional data from both computer and physical experiments has gained increasing attention due to the dynamic nature of many engineering systems. However, the complexity and huge amount of functional data bring many difficulties to apply traditional or existing methodologies. The objective of the present study is twofold: (1) prediction of functional responses based on functional data and (2) prediction of bias function for validation of a computer model that predicts functional responses. In this paper, we first develop a functional regression model with linear basis functions to analyze functional data. Then combining data from both computer and physical experiments, we use the functional analysis modeling to predict the bias function which is crucial for validating a computer model. The proposed method, following the classical nonparametric regression framework, uses a single step procedure which is easily implemented and computationally efficient. Through an application example of motor engine analysis to predict acceleration performance and gear shift events, we demonstrate our approach and compare it to using the Gaussian process modeling approach.

关键词： functional response model validation functional regression model nonparametric regression validation metric model updating

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functional CLUSTERING FOR LONGITUDINAL ASSOCIATIONS BETWEEN SOCIAL DETERMINANTS OF HEALTH AND STROKE MORTALITY IN THE U.S.

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Annals of Applied Statistics 2025年第1期19卷 798-820页

作者： Luo, Fangzhi Tan, Jianbin Zhang, Donglan Huang, Hui Shen, Ye Department of Epidemiology and Biostatistics College of Public Health University of Georgia United States Department of Biostatistics and Bioinformatics School of Medicine Duke University United States Department of Foundations of Medicine NYU Grossman Long Island School of Medicine United States Center for Applied Statistics and School of Statistics Renmin University of China China

Understanding the longitudinally changing associations between Social Determinants of Health (SDOH) and stroke mortality is essential for effective stroke management. Previous studies have uncovered significant regional disparities in the associations between SDOH and stroke mortality. However, existing studies have not utilized longitudinal associations to develop datadriven methods for regional division in stroke control. To fill this gap, we propose a novel clustering method to analyze SDOH-stroke mortality associations across U.S. counties. To enhance the interpretability of the clustering outcomes, we introduce a novel regularized expectation-maximization algorithm equipped with sparsity-and smoothness-pursued penalties, aiming at simultaneous clustering and variable selection in longitudinal associations. As a result, we can identify key SDOH that contributes to longitudinal changes in stroke mortality. This facilitates the clustering of U.S. counties based on the associations between these SDOH and stroke mortality. The effectiveness of our proposed method is demonstrated through extensive numerical studies. By applying our method to longitudinal data on SDOH and stroke mortality at the county level, we identify 18 important SDOH for stroke mortality and divide the U.S. counties into two clusters based on these selected SDOH. Our findings unveil complex regional heterogeneity in the longitudinal associations between SDOH and stroke mortality, providing valuable insights into region-specific SDOH adjustments for mitigating stroke mortality. © Institute of Mathematical Statistics, 2025.

关键词： functional regression model model-based clustering regularized expectation-maximization algorithm stroke mortality variable selection

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High leverage detection in general functional regression models with spatially correlated errors

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APPLIED STOCHASTIC modelS IN BUSINESS AND INDUSTRY 2022年第1期38卷 169-181页

作者： Romano, Elvira Giraldo, Ramon Mateu, Jorge Diana, Andrea Univ Campania Luigi Vanvitelli Dept Math & Phys Caserta Italy Univ Nacl Colombia Sci Fac Dept Stat Bogota Colombia Univ Jaume 1 Dept Math Castellon de La Plana Spain

The presence of curves that deviate markedly from the core of a set of curves can greatly affect inference and forecasting in a functional regression model. Thus their detection is key to increase the accuracy of the required estimates. This work introduces the concepts of high leverage in general functional regression models with independent and spatially correlated errors. The projection matrix, also known as Hat matrix, plays a crucial role in classical model diagnosis, since it provides a measure of leverage. We propose a generalisation of the projection matrix in both the functional and the spatial functional frameworks under two settings, when the response variable is a scalar, and when it is a function itself, the so-called total model. Commonly used influence measures are also proposed as functions of the generalised functional leverages and residuals. An application of the proposed procedures for investigating the effect of outliers on the relationship between transformation of the banking industry and the size of cooperative banks in Italy over a period of 14 years is presented.

关键词： functional data functional regression model geostatistics hat matrix high leverage outlier spatial dependence structure

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Simultaneous confidence bands for functional regression models

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2017年 188卷 67-81页

作者： Chang, Chung Lin, Xuejing Ogden, R. Todd Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung Taiwan Columbia Univ Dept Biostat New York NY USA

In recent years, the field of functional data analysis (FDA) has received a great deal of attention, and many useful theories and interesting applications have been reported. One topic of particular interest involves estimation of simultaneous confidence bands (SCB) for an unknown function. Degras (2011) proposed an estimator of SCBs for the mean function in a simple (no covariates) function-on-scalar regression model that relies on some assumptions on the tail behavior of the errors. In the case that such distributional assumptions do not hold, Degras also proposed a bootstrap method (sampling with replacement). We consider a more general function-on-scalar regression model that involves multiple covariates and allows the variance function of the functional responses to be dependent on the covariates (heterogeneity). In this general model, we propose a wild bootstrap method for estimating SCBs for the coefficient function. Some asymptotic results are provided for the simple case (no covariates) and simulation results for both the simple and general models. (C) 2017 Elsevier B.V. All rights reserved.

关键词： functional regression model Wild bootstrap Simultaneous confidence bands

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Robust depth-based estimation of the functional autoregressive model

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 131卷 66-79页

作者： Martinez-Hernandez, Israel Genton, Marc G. Gonzalez-Farias, Graciela King Abdullah Univ Sci & Technol Stat Program Thuwal 239556900 Saudi Arabia Ctr Invest Matemat AC Jalisco S-N Guanajuato 36240 Mexico

A robust estimator for functional autoregressive models is proposed, the Depth-based Least Squares (DLS) estimator. The DLS estimator down-weights the influence of outliers by using the functional directional outlyingness as a centrality measure. It consists of two steps: identifying the outliers with a two-stage functional boxplot, then down-weighting the outliers using the functional directional outlyingness. Theoretical properties of the DLS estimator are investigated such as consistency and boundedness of its influence function. Through a Monte Carlo study, it is shown that the DLS estimator performs better than estimators based on Principal Component Analysis (PCA) and robust PCA, which are the most commonly used. To illustrate a practical application, the DLS estimator is used to analyze a dataset of ambient CO(2 )concentrations in California. (C) 2018 Elsevier B.V. All rights reserved.

关键词： functional autoregression model functional data analysis functional regression model functional time series Influence function Robust estimator

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