Integrated Depths for Partially Observed Functional Data

References

• Arribas-Gil, A., and Romo, J. (2014), “Shape Outlier Detection and Visualization for Functional Data: The Outliergram,” Biostatistics, 15, 603–619. DOI: 10.1093/biostatistics/kxu006.
   PubMed Web of Science ®Google Scholar
• Claeskens, G., Hubert, M., Slaets, L., and Vakili, K. (2014), “Multivariate Functional Halfspace Depth,” Journal of the American Statistical Association, 109, 411–423. DOI: 10.1080/01621459.2013.856795.
   Web of Science ®Google Scholar
• Cuesta-Albertos, J. A., Febrero-Bande, M., and Oviedo de la Fuente, M. (2017), “The DDg-Classifier in the Functional Setting,” TEST, 26, 119–142.
   Web of Science ®Google Scholar
• Dai, W., and Genton, M. G. (2018), “Functional Boxplots for Multivariate Curves,” Stat, 7, e190, 10. DOI: 10.1002/sta4.190.
   Web of Science ®Google Scholar
• Dai, W., Mrkvička, T., Sun, Y., and Genton, M. G. (2020), “Functional Outlier Detection and Taxonomy by Sequential Transformations,” Computational Statistics & Data Analysis, 149, 106960.
   Web of Science ®Google Scholar
• D’Amato, V., Piscopo, G., and Russolillo, M. (2011), “The Mortality of the Italian Population: Smoothing Techniques on the Lee-Carter Model,” Annals of Applied Statistics, 5, 705–724.
   Web of Science ®Google Scholar
• Delaigle, A., and Hall, P. (2013), “Classification Using Censored Functional Data,” Journal of the American Statistical Association, 108, 1269–1283. DOI: 10.1080/01621459.2013.824893.
   Web of Science ®Google Scholar
• Delaigle, A., and Hall, P. (2016), “Approximating Fragmented Functional Data by Segments of Markov Chains,” Biometrika, 103, 779–799.
   Web of Science ®Google Scholar
• Di, C., Crainiceanu, C. M., and Jank, W. S. (2014), “Multilevel Sparse Functional Principal Component Analysis,” Stat, 3, 126–143. DOI: 10.1002/sta4.50.
   PubMedGoogle Scholar
• Duveiller, G., Fasbender, D., and Meroni, M. (2016), “Revisiting the Concept of a Symmetric Index of Agreement for Continuous Datasets,” Scientific Reports, 6, 19401. DOI: 10.1038/srep19401.
   PubMed Web of Science ®Google Scholar
• Elías, A., Jiménez, R., Paganoni, A., and Sangalli, L. (2021), fdaPOIFD: Partially Observed Integrated Functional Depth, R package version 1.0.2. DOI: 10.1080/10618600.2022.2070171.
   Google Scholar
• Febrero-Bande, M., Galeano, P., and González-Manteiga, W. (2008), “Outlier Detection in Functional Data by Depth Measures, with Application to Identify Abnormal Nox Levels,” Environmetrics, 19, 331–345. DOI: 10.1002/env.878.
   Web of Science ®Google Scholar
• Fraiman, R., and Muniz, G. (2001). “Trimmed Means for Functional Data,” Test, 10, 419–440. DOI: 10.1007/BF02595706.
   Web of Science ®Google Scholar
• Genton, M. G., Johnson, C., Potter, K., Stenchikov, G., and Sun, Y. (2014), “Surface Boxplots,” Stat, 3, 1–11. DOI: 10.1002/sta4.39.
   PubMedGoogle Scholar
• Gijbels, I., and Nagy, S. (2017), “On a General Definition of Depth for Functional Data,” Statistical Science, 32, 630–639. DOI: 10.1214/17-STS625.
   Web of Science ®Google Scholar
• Goldberg, Y., Ritov, Y., and Mandelbaum, A. (2014), “Predicting the Continuation of a Function with Applications to Call Center Data,” Journal of Statistical Planning and Inference, 147, 53–65. DOI: 10.1016/j.jspi.2013.11.006.
   Web of Science ®Google Scholar
• Goldsmith, J., Greven, S., and Crainiceanu, C. (2013), “Corrected Confidence Bands for Functional Data Using Principal Components,” Biometrics, 69, 41–51. DOI: 10.1111/j.1541-0420.2012.01808.x.
   PubMed Web of Science ®Google Scholar
• Hubert, M., Rousseeuw, P., and Segaert, P. (2017), “Multivariate and Functional Classification Using Depth and Distance,” Advances in Data Analysis and Classification, 11, 445–466. DOI: 10.1007/s11634-016-0269-3.
   Web of Science ®Google Scholar
• Hubert, M., Rousseeuw, P. J., and Vanden Branden, K. (2005), “Robpca: A New Approach to Robust Principal Component Analysis,” Technometrics, 47, 64–79. DOI: 10.1198/004017004000000563.
   Web of Science ®Google Scholar
• Human Mortality Database. (2019), “University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany),” Available at www.mortality.org.
   Google Scholar
• Hyndman, R. J., and Shang, H. L. (2010), “Rainbow Plots, Bagplots, and Boxplots for Functional Data,” Journal of Computational & Graphical Statistics, 19, 29–45.
   Web of Science ®Google Scholar
• Ieva, F., and Paganoni, A. M. (2013), “Depth Measures for Multivariate Functional Data,” Communications in Statistics - Theory and Methods, 42, 1265–1276. DOI: 10.1080/03610926.2012.746368.
   Web of Science ®Google Scholar
• Ieva, F., and Paganoni, A. M. (2017), “Component-Wise Outlier Detection Methods for Robustifying Multivariate Functional Samples,” Statistical Papers, 61, 595–614.
   Google Scholar
• James, G., Hastie, T., and Sugar, C. (2000), “Principal Component Models for Sparse Functional Data,” Biometrika, 87, 587–602. DOI: 10.1093/biomet/87.3.587.
   Web of Science ®Google Scholar
• James, G. M., and Hastie, T. J. (2001), “Functional Linear Discriminant Analysis for Irregularly Sampled Curves,” Journal of the Royal Statistical Society, Series B, 63, 533–550. DOI: 10.1111/1467-9868.00297.
   Google Scholar
• Kneip, A., and Liebl, D. (2020), “On the Optimal Reconstruction of Partially Observed Functional Data,” The Annals of Statistics, 48, 1692–1717. DOI: 10.1214/19-AOS1864.
   Web of Science ®Google Scholar
• Kraus, D. (2015), “Components and Completion of Partially Observed Functional Data,” Journal of the Royal Statistical Society, Series B, 77, 777–801. DOI: 10.1111/rssb.12087.
   Google Scholar
• Kraus, D., and Stefanucci, M. (2019), “Classification of Functional Fragments by Regularized Linear Classifiers with Domain Selection,” Biometrika, 106, 161–180. DOI: 10.1093/biomet/asy060.
   Web of Science ®Google Scholar
• Li, J., Cuesta-Albertos, J. A., and Liu, R. Y. (2012), “Dd-Classifier: Nonparametric Classification Procedure Based on dd-plot,” Journal of the American Statistical Association, 107, 737–753. DOI: 10.1080/01621459.2012.688462.
   Web of Science ®Google Scholar
• Liebl, D. (2019), “Nonparametric Testing for Differences in Electricity Prices: The Case of the Fukushima Nuclear Accident,”’ The Annals of Applied Statistics, 2, 1128–1146. DOI: 10.1214/18-AOAS1230.
   Google Scholar
• Liebl, D., and Rameseder, S. (2019), “Partially Observed Functional Data: The Case of Systematically Missing Parts,” Computational Statistics & Data Analysis, 131, 104–115.
   Web of Science ®Google Scholar
• Lin, Z., Wang, J.-L., and Zhong, Q. (2020), “Basis Expansions for Functional Snippets,” Biometrika, 108, 709–726. DOI: 10.1093/biomet/asaa088.
   Web of Science ®Google Scholar
• Liu, C., Ray, S., and Hooker, G. (2017), “Functional Principal Component Analysis of Spatially Correlated Data,” Statistics and Computing, 27, 1639–1654. DOI: 10.1007/s11222-016-9708-4.
   Web of Science ®Google Scholar
• Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T., Cohen, K. L., Boente, G., Fraiman, R., Brumback, B., Croux, C., Fan, J., Kneip, A., Marden, J. I., Peña, D., Prieto, J., Ramsay, J. O., Valderrama, M. J., Aguilera, A. M., Locantore, N., Marron, J. S., Simpson, D. G., Tripoli, N., Zhang, J. T., and Cohen, K. L. (1999), “Robust Principal Component Analysis for Functional Data,” Test, 8, 1–73. DOI: 10.1007/BF02595862.
   Web of Science ®Google Scholar
• López-Pintado, S., and Romo, J. (2009), “On the Concept of Depth for Functional Data,” Journal of the American Statistical Association, 104, 718–734. DOI: 10.1198/jasa.2009.0108.
   Web of Science ®Google Scholar
• López-Pintado, S., and Romo, J. (2011), “A Half-Region Depth for Functional Data,” Computational Statistics & Data Analysis, 55, 1679–1695.
   Web of Science ®Google Scholar
• Nagy, S., Gijbels, I., and Hlubinka, D. (2017), “Depth-Based Recognition of Shape Outlying Functions,” Journal of Computational & Graphical Statistics, 26, 883–893.
   Web of Science ®Google Scholar
• Nagy, S., Gijbels, I., Omelka, M., and Hlubinka, D. (2016), “Integrated Depth for Functional Data: Statistical Properties and Consistency,” ESAIM. Probability and Statistics, 20, 95–130. DOI: 10.1051/ps/2016005.
   Web of Science ®Google Scholar
• Narisetty, N. N., and Nair, V. N. (2015), “Extremal Depth for Functional Data and Applications,” Journal of the American Statistical Association, 111, 1705–1714. DOI: 10.1080/01621459.2015.1110033.
   Web of Science ®Google Scholar
• Nieto-Reyes, A., and Battey, H. (2016), “A Topologically Valid Definition of Depth for Functional Data,” Statistical Science, 31, 61–79. DOI: 10.1214/15-STS532.
   Web of Science ®Google Scholar
• Qu, Z., and Genton. M. G. (2022), “Sparse Functional Boxplots for Multivariate Curves,” Journal of Computational and Graphical Statistics, 1–30. DOI: 10.1080/10618600.2022.2066680.
   Web of Science ®Google Scholar
• Sangalli, L. M., Secchi, P., and Vantini, S. (2014a), “Analysis of Aneurisk65 Data: k-mean Alignment,” Electronic Journal of Statistics, 8, 1891–1904. DOI: 10.1214/14-EJS938A.
   Web of Science ®Google Scholar
• Sangalli, L. M., Secchi, P., and Vantini, S. (2014b), “Aneurisk65: A Dataset of Three-Dimensional Cerebral Vascular Geometries,” Electronic Journal of Statistics, 8, 1879–1890.
   Web of Science ®Google Scholar
• Sangalli, L. M., Secchi, P., Vantini, S., and Veneziani, A. (2009), “A Case Study in Exploratory Functional Data Analysis: Geometrical Features of the Internal Carotid Artery,” Journal of the American Statistical Association, 104, 37–48. DOI: 10.1198/jasa.2009.0002.
   Web of Science ®Google Scholar
• Sangalli, L. M., Secchi, P., Vantini, S., and Vitelli, V. (2010), “k-mean Alignment for Curve Clustering,” Computational Statistics & Data Analysis, 54, 1219–1233.
   Web of Science ®Google Scholar
• Sguera, C., and López-Pintado, S. (2020), “A Notion of Depth for Sparse Functional Data,” TEST, 30, 630–649. DOI: 10.1007/s11749-020-00734-y.
   Web of Science ®Google Scholar
• Stefanucci, M., Sangalli, L. M., and Brutti, P. (2018), “Pca-Based Discrimination of Partially Observed Functional Data, with an Application to Aneurisk65 Data Set,” Statistica Neerlandica, 72, 246–264. DOI: 10.1111/stan.12137.
   Web of Science ®Google Scholar
• Sun, Y., and Genton, M. G. (2011), “Functional Boxplots,” Journal of Computational & Graphical Statistics, 20, 316–334.
   Web of Science ®Google Scholar
• Sun, Y., and Genton, M. G. (2012), “Adjusted Functional Boxplots for Spatio-Temporal Data Visualization and Outlier Detection,” Environmetrics, 23, 54–64.
   Web of Science ®Google Scholar
• Yao, F., Muller, H.-G., and Wang, J.-L. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590. DOI: 10.1198/016214504000001745.
   Web of Science ®Google Scholar