Second-Generation Functional Data

Koner, Salil; Staicu, Ana‐Maria

doi:10.1146/annurev-statistics-032921-033726

Cited by 15 publications

(1 citation statement)

References 106 publications

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“…Goldsmith et al (2012)). Approaches that account for dependence within subject or cluster have been discussed by Greven et al (2010); ; Park and Staicu (2015); Koner and Staicu (2023), to name a few.…”

Section: Covariates Observed With Noisementioning

confidence: 99%

A bias-adjusted estimator in quantile regression for clustered data

Battagliola

Sørensen

Tolver

et al. 2022

Econometrics and Statistics

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Section: Covariates Observed With Noisementioning

confidence: 99%

A bias-adjusted estimator in quantile regression for clustered data

Battagliola

Sørensen

Tolver

et al. 2022

Econometrics and Statistics

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Functional Data Analysis: An Introduction and Recent Developments

Gertheiss,

Rügamer,

Liew

et al. 2024

Biometrical J

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Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub.

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Functional data analysis using deep neural networks

Wang,

Zhang,

Cao

et al. 2024

WIREs Computational Stats

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Functional data analysis is an evolving field focused on analyzing data that reveals insights into curves, surfaces, or entities within a continuous domain. This type of data is typically distinguished by the inherent dependence and smoothness observed within each data curve. Traditional functional data analysis approaches have predominantly relied on linear models, which, while foundational, often fall short in capturing the intricate, nonlinear relationships within the data. This paper seeks to bridge this gap by reviewing the integration of deep neural networks into functional data analysis. Deep neural networks present a transformative approach to navigating these complexities, excelling particularly in high‐dimensional spaces and demonstrating unparalleled flexibility in managing diverse data constructs. This review aims to advance functional data regression, classification, and representation by integrating deep neural networks with functional data analysis, fostering a harmonious and synergistic union between these two fields. The remarkable ability of deep neural networks to adeptly navigate the intricate functional data highlights a wealth of opportunities for ongoing exploration and research across various interdisciplinary areas.This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical Learning and Exploratory Methods of the Data Sciences > Neural Networks

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Second-Generation Functional Data

Cited by 15 publications

References 106 publications

A bias-adjusted estimator in quantile regression for clustered data

A bias-adjusted estimator in quantile regression for clustered data

Functional Data Analysis: An Introduction and Recent Developments

Functional data analysis using deep neural networks

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