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Szarek D, Maraj-Zygmąt K, Sikora G, Krapf D, Wyłomańska A. Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2021.107401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Striegel C, Biehler J, Wall WA, Kauermann G. A Multifidelity Function-on-Function Model applied to an Abdominal Aortic Aneurysm. Technometrics 2022. [DOI: 10.1080/00401706.2021.2024453] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Christoph Striegel
- Department of Statistics, Ludwig-Maximilians-Universität München, 80539 München, Germany
| | - Jonas Biehler
- Department of Mechanical Engineering, Technische Universität München, 85748 Garching bei München, Germany
| | - Wolfgang A. Wall
- Department of Mechanical Engineering, Technische Universität München, 85748 Garching bei München, Germany
| | - Göran Kauermann
- Department of Statistics, Ludwig-Maximilians-Universität München, 80539 München, Germany
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Abstract
Summary
It is common to want to regress a scalar response on a random function. This paper presents results that advocate local linear regression based on a projection as a nonparametric approach to this problem. Our asymptotic results demonstrate that functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object in its own right. The local linear estimator of the functional derivative is shown to be consistent. For both the estimator of the regression functional and the estimator of its derivative, theoretical properties are detailed. On simulated datasets we illustrate good finite-sample properties of the proposed methods. On a real data example of a single-functional index model, we indicate how the functional derivative of the regression operator provides an original, fast and widely applicable estimation method.
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Affiliation(s)
- F Ferraty
- Toulouse Mathematics Institute, University of Toulouse, 118 route de Narbonne, 31062 Toulouse cedex, France
| | - S NAGY
- Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic
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Chen J, Mak S, Joseph VR, Zhang C. Function-on-Function Kriging, With Applications to Three-Dimensional Printing of Aortic Tissues. Technometrics 2020. [DOI: 10.1080/00401706.2020.1801255] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Jialei Chen
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA
- Georgia Tech Manufacturing Institute, Georgia Institute of Technology, Atlanta, GA
| | - Simon Mak
- Department of Statistical Science, Duke University, Durham, NC
| | - V. Roshan Joseph
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA
| | - Chuck Zhang
- H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA
- Georgia Tech Manufacturing Institute, Georgia Institute of Technology, Atlanta, GA
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5
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De Iaco S, Posa D, Cappello C, Maggio S. On Some Characteristics of Gaussian Covariance Functions. Int Stat Rev 2020. [DOI: 10.1111/insr.12403] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Sandra De Iaco
- Dipartimento di Scienze dell'Economia Università del Salento, Complesso Ecotekne, Via per Monteroni Lecce Italia
| | - Donato Posa
- Dipartimento di Scienze dell'Economia Università del Salento, Complesso Ecotekne, Via per Monteroni Lecce Italia
| | - Claudia Cappello
- Dipartimento di Scienze dell'Economia Università del Salento, Complesso Ecotekne, Via per Monteroni Lecce Italia
| | - Sabrina Maggio
- Dipartimento di Scienze dell'Economia Università del Salento, Complesso Ecotekne, Via per Monteroni Lecce Italia
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Ferraty F, Kokoszka P, Wang JL, Wu Y. Editorial for the special issue on High-dimensional and functional data analysis. Comput Stat Data Anal 2019. [DOI: 10.1016/j.csda.2018.10.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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