Recent advances in functional data analysis and high-dimensional statistics

Aneiros, Germán; Cao, Ricardo; Fraiman, Ricardo; Genest, Christian; Vieu, Philippe

doi:10.1016/j.jmva.2018.11.007

Cited by 133 publications

(38 citation statements)

References 104 publications

(139 reference statements)

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“…FDA is a matured field in the area of statistics, with focus on bases in functional spaces such as polynomials, wavelets and others. Maturity of the field can be observed by recent review papers [7] or special issues [8] in prestigious journals covering the field of statistics. We join FDA with Bayesian approach in order to obtain probability distributions of basis coefficients, get generative models and model uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Recognizing VSC DC Cable Fault Types Using Bayesian Functional Data Depth

2021

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Diagnostics of power and energy systems is obviously an important matter. In this paper we present a contribution of using new methodology for the purpose of signal type recognition (for example, faulty/healthy or different types of faults). Our approach uses Bayesian functional data analysis with data depths distributions to detect differing signals. We present our approach for discrimination of pole-to-pole and pole-to-ground short circuits in VSC DC cables. We provide a detailed case study with Monte Carlo analysis. Our results show potential for applications in diagnostics under uncertainty.

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Section: Introductionmentioning

confidence: 99%

Recognizing VSC DC Cable Fault Types Using Bayesian Functional Data Depth

2021

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“…In the state-of-the-art literature, (Kokoszka and Reimherr 2017) provided an excellent introduction of the most fundamental concepts of FDA methodology and relevant FDA techniques. (Aneiros et al 2018) prepared an organized overview of recent advances in high-dimensional statistics and functional data analysis with a concise survey of the related topics and (Wang et al 2015) provided a detailed overview of functional data analysis (FDA) techniques. Regarding the specialized literature on the functional principal component analysis (FPCA), (Hall 2011) discussed the theory and methodology of principal component analysis (PCA) for functional data besides (Shang 2014) reviewed and described the roles of functional principal component analysis (FPCA) in exploratory analysis of functional data.…”

Section: Introductionmentioning

confidence: 99%

Modeling of rainfall variability using functional principal component method: a case study of Taiz region, Yemen

Hael

2020

Model. Earth Syst. Environ.

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The sophisticated functional techniques can efficiently analyze and model various earth systems, such as the climate change system. The major objective of this study is to adapt the functional principal component analysis (FPCA) method for rainfall data to capture the variations over time intervals and establish a functional model of the rainfall patterns. Furthermore, this work contributes to discovering and modeling the main rainfall features. It could be useful for a better understanding of the Taiz region's rainfall regime during the past 2 decades. The analysis was conducted according to the average monthly rainfall of the Taiz region from 1998 to 2019 and processed using R software. The proposed approach of functional principal components has been successfully carried out and demonstrated significant findings for rainfall patterns and temporal variations. According to the results of the current study, the first four functional principal components illustrated 33%, 23.3%, 17.3%, and 13.3% of the total variance of the rainfall variability, respectively. Moreover, the FPCs model showed that the amount of rainfall over the Taiz region during the last 2 decades has influenced by the monsoonal intertropical and Red Sea convergence zones.

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“…So, the quantitative structure of the FDA approach could be viewed as an acceptable methodology with a specific perspective compared to traditional statistical analyses [11][12][13][14]. Many contributions cover a wide range of statistical problems involving the FDA such as mathematical foundations, covariance operator estimation, functional depth, functional autoregressive processes, linear regression [15,16], semiparametric regression, nonparametric regression, spatial functional statistics, robust functional data analysis as well as sparsity in FDA [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Visualization of rainfall data using functional data analysis

2020

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In recent years, functional data analysis (FDA) has been used in many applications in order to analyze data that provide detail on curves, surfaces or other components of a continuum. The purpose of this research is mainly to incorporate and adapt visualization tools for the FDA of rainfall in the Taiz Region. Moreover, visualizing the temporal variations of rainfall in order to provide a clear understanding of the rainfall patterns and also to help in predicting the future. The current study has been conducted based on average monthly rainfall over the Taiz Region during the period of 1998-2018. The R software was used to process the data obtained from the Tropical Rainfall Measuring Mission in Taiz City. The functional rainfall data have been smoothed using penalized smoothing according to generalized cross-validation criteria. The results showed that the rainfall profiles in the Taiz Region depend significantly on their temporal locations due to the monsoonal influences, which reflect the distribution of rains in the spring and the summer seasons.

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Recent advances in functional data analysis and high-dimensional statistics

Cited by 133 publications

References 104 publications

Recognizing VSC DC Cable Fault Types Using Bayesian Functional Data Depth

Recognizing VSC DC Cable Fault Types Using Bayesian Functional Data Depth

Modeling of rainfall variability using functional principal component method: a case study of Taiz region, Yemen

Visualization of rainfall data using functional data analysis

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