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Arnone E, Sangalli LM, Vicini A. Smoothing spatio-temporal data with complex missing data patterns. STAT MODEL 2021. [DOI: 10.1177/1471082x211057959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
We consider spatio-temporal data and functional data with spatial dependence, characterized by complicated missing data patterns. We propose a new method capable to efficiently handle these data structures, including the case where data are missing over large portions of the spatio-temporal domain. The method is based on regression with partial differential equation regularization. The proposed model can accurately deal with data scattered over domains with irregular shapes and can accurately estimate fields exhibiting complicated local features. We demonstrate the consistency and asymptotic normality of the estimators. Moreover, we illustrate the good performances of the method in simulations studies, considering different missing data scenarios, from sparse data to more challenging scenarios where the data are missing over large portions of the spatial and temporal domains and the missing data are clustered in space and/or in time. The proposed method is compared to competing techniques, considering predictive accuracy and uncertainty quantification measures. Finally, we show an application to the analysis of lake surface water temperature data, that further illustrates the ability of the method to handle data featuring complicated patterns of missingness and highlights its potentiality for environmental studies.
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Affiliation(s)
- Eleonora Arnone
- MOX ’ Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
| | - Laura M. Sangalli
- MOX ’ Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
| | - Andrea Vicini
- MOX ’ Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
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Liu X, Yeo K, Hwang Y, Singh J, Kalagnanam J. A statistical modeling approach for air quality data based on physical dispersion processes and its application to ozone modeling. Ann Appl Stat 2016. [DOI: 10.1214/15-aoas901] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Berrett C, Williams GP, Moon T, Gunther J. A Bayesian Nonparametric Model for Temperature-Emissivity Separation of Long-Wave Hyperspectral Images. Technometrics 2014. [DOI: 10.1080/00401706.2013.869262] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Sigrist F, Künsch HR, Stahel WA. Stochastic partial differential equation based modelling of large space-time data sets. J R Stat Soc Series B Stat Methodol 2014. [DOI: 10.1111/rssb.12061] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabio Sigrist
- Eidgenössiche Technische Hochschule Zürich; Switzerland
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Malmberg A, Arellano A, Edwards DP, Flyer N, Nychka D, Wikle C. Interpolating fields of carbon monoxide data using a hybrid statistical-physical model. Ann Appl Stat 2008. [DOI: 10.1214/08-aoas168] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Fuentes M, Guttorp P, Stein ML. Special section on statistics in the atmospheric sciences. Ann Appl Stat 2008. [DOI: 10.1214/08-aoas209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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