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Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference

Citations

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Cited by:

  1. Park, Juhyun & Gasser, Theo & Rousson, Valentin, 2009. "Structural components in functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3452-3465, July.
  2. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
  3. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
  4. Shang, Han Lin & Hyndman, Rob.J., 2011. "Nonparametric time series forecasting with dynamic updating," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1310-1324.
  5. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
  6. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
  7. Benatia, David & Carrasco, Marine & Florens, Jean-Pierre, 2017. "Functional linear regression with functional response," Journal of Econometrics, Elsevier, vol. 201(2), pages 269-291.
  8. Sven Otto & Nazarii Salish, 2022. "Approximate Factor Models for Functional Time Series," Papers 2201.02532, arXiv.org, revised May 2024.
  9. Fekri, M. & Ruiz-Gazen, A., 2004. "Robust weighted orthogonal regression in the errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 89-108, January.
  10. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
  11. Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
  12. Peijun Sang & Liangliang Wang & Jiguo Cao, 2017. "Parametric functional principal component analysis," Biometrics, The International Biometric Society, vol. 73(3), pages 802-810, September.
  13. Biau Gérard & Mas André, 2012. "PCA-kernel estimation," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 19-46, March.
  14. Ana Aguilera & Francisco Ocaña & Mariano Valderrama, 1999. "Forecasting with unequally spaced data by a functional principal component approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 233-253, June.
  15. Kneip, Alois & Benko, Michal, 2005. "Common functional component modelling," SFB 649 Discussion Papers 2005-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  16. repec:cte:wsrepe:ws1506 is not listed on IDEAS
  17. Enzo Giacomini & Wolfgang Härdle & Volker Krätschmer, 2009. "Dynamic semiparametric factor models in risk neutral density estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(4), pages 387-402, December.
  18. Xiao, Sinan & Lu, Zhenzhou & Xu, Liyang, 2017. "Multivariate sensitivity analysis based on the direction of eigen space through principal component analysis," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 1-10.
  19. Graciela Boente & Daniela Rodriguez & Mariela Sued, 2018. "Testing equality between several populations covariance operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 919-950, August.
  20. Salish, Nazarii & Gleim, Alexander, 2019. "A moment-based notion of time dependence for functional time series," Journal of Econometrics, Elsevier, vol. 212(2), pages 377-392.
  21. Haixu Wang & Jiguo Cao, 2023. "Nonlinear prediction of functional time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
  22. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
  23. Romain, Yves, 2002. "Perturbation of functional tensors with applications to covariance operators," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 253-264, July.
  24. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
  25. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
  26. Andrii Babii & Eric Ghysels & Junsu Pan, 2022. "Tensor Principal Component Analysis," Papers 2212.12981, arXiv.org, revised Aug 2023.
  27. Bali, Juan Lucas & Boente, Graciela, 2014. "Consistency of a numerical approximation to the first principal component projection pursuit estimator," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 181-191.
  28. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
  29. Christian Acal & Manuel Escabias & Ana M. Aguilera & Mariano J. Valderrama, 2021. "COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression," Mathematics, MDPI, vol. 9(11), pages 1-23, May.
  30. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
  31. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
  32. Mas, André, 2006. "A sufficient condition for the CLT in the space of nuclear operators--Application to covariance of random functions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1503-1509, August.
  33. André Mas, 2002. "Testing for the Mean of Random Curves : from Penalization to Dimension Selection," Working Papers 2002-08, Center for Research in Economics and Statistics.
  34. repec:hum:wpaper:sfb649dp2005-016 is not listed on IDEAS
  35. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
  36. Justin Petrovich & Matthew Reimherr & Carrie Daymont, 2022. "Highly irregular functional generalized linear regression with electronic health records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 806-833, August.
  37. Nie, Yunlong & Cao, Jiguo, 2020. "Sparse functional principal component analysis in a new regression framework," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
  38. Rademacher, Daniel & Kreiß, Jens-Peter & Paparoditis, Efstathios, 2024. "Asymptotic normality of spectral means of Hilbert space valued random processes," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
  39. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
  40. Jarry, Gabriel & Delahaye, Daniel & Nicol, Florence & Feron, Eric, 2020. "Aircraft atypical approach detection using functional principal component analysis," Journal of Air Transport Management, Elsevier, vol. 84(C).
  41. Ocaña, F. A. & Aguilera, A. M. & Valderrama, M. J., 1999. "Functional Principal Components Analysis by Choice of Norm," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 262-276, November.
  42. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2010. "Inference under functional proportional and common principal component models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 464-475, February.
  43. G. Gaines & K. Kaphle & F. Ruymgaart, 2014. "A Note on Random Perturbations of a Multiple Eigenvalue of a Hermitian Operator," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1112-1123, December.
  44. Cai, Leheng & Hu, Qirui, 2024. "Simultaneous inference and uniform test for eigensystems of functional data," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
  45. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
  46. Bali, Juan Lucas & Boente, Graciela, 2017. "Robust estimators under a functional common principal components model," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 424-440.
  47. Cees Diks & Bram Wouters, 2023. "Noise reduction for functional time series," Papers 2307.02154, arXiv.org.
  48. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
  49. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
  50. Han Lin Shang, 2010. "Nonparametric modeling and forecasting electricity demand: an empirical study," Monash Econometrics and Business Statistics Working Papers 19/10, Monash University, Department of Econometrics and Business Statistics.
  51. repec:hum:wpaper:sfb649dp2006-010 is not listed on IDEAS
  52. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
  53. Santiago Gall n & Jorge Barrientos, 2021. "Forecasting the Colombian Electricity Spot Price under a Functional Approach," International Journal of Energy Economics and Policy, Econjournals, vol. 11(2), pages 67-74.
  54. Vladimir Koltchinskii & Karim Lounici, 2017. "New Asymptotic Results in Principal Component Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 254-297, August.
  55. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
  56. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.
  57. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
  58. Ana M. Aguilera, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 23-26, March.
  59. Lamboni, Matieyendou & Monod, Hervé & Makowski, David, 2011. "Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 450-459.
  60. Heungsun Hwang & Hye Suk & Yoshio Takane & Jang-Han Lee & Jooseop Lim, 2015. "Generalized Functional Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 101-125, March.
  61. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
  62. Ellingson, Leif & Patrangenaru, Vic & Ruymgaart, Frits, 2013. "Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 317-333.
  63. Lixia Hu & Baolin Chen & Jinhong You, 2024. "Locally sparse estimator for functional linear panel models with fixed effects," Statistical Papers, Springer, vol. 65(9), pages 5753-5773, December.
  64. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
  65. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
  66. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
  67. van Delft, Anne, 2020. "A note on quadratic forms of stationary functional time series under mild conditions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4206-4251.
  68. Christoph Hellmayr & Alan E. Gelfand, 2021. "A Partition Dirichlet Process Model for Functional Data Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 30-65, May.
  69. Christian Acal & Ana M. Aguilera & Manuel Escabias, 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
  70. Cupidon, J. & Eubank, R. & Gilliam, D. & Ruymgaart, F., 2008. "Some properties of canonical correlations and variates in infinite dimensions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1083-1104, July.
  71. Li, Yehua & Hsing, Tailen, 2007. "On rates of convergence in functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1782-1804, October.
  72. Bauer, Jan O. & Drabant, Bernhard, 2023. "Regression based thresholds in principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
  73. Ana Aguilera, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 23-26, March.
  74. Bali, Juan Lucas & Boente, Graciela, 2015. "Influence function of projection-pursuit principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 173-199.
  75. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
  76. Lee, Seokho & Shin, Hyejin & Billor, Nedret, 2013. "M-type smoothing spline estimators for principal functions," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 89-100.
  77. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
  78. Bauer, Jan O. & Drabant, Bernhard, 2021. "Principal loading analysis," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
  79. Beran, Jan & Liu, Haiyan, 2016. "Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 218-233.
  80. Qi, Xin & Zhao, Hongyu, 2011. "Some theoretical properties of Silverman's method for Smoothed functional principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 741-767, April.
  81. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
  82. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
  83. Haolun Shi & Jiguo Cao, 2022. "Robust Functional Principal Component Analysis Based on a New Regression Framework," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 523-543, September.
  84. Tingting Huang & Gilbert Saporta & Huiwen Wang & Shanshan Wang, 2021. "A robust spatial autoregressive scalar-on-function regression with t-distribution," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 57-81, March.
  85. Fraiman, Ricardo & Gimenez, Yanina & Svarc, Marcela, 2016. "Feature selection for functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 191-208.
  86. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
  87. Munk, A. & Paige, R. & Pang, J. & Patrangenaru, V. & Ruymgaart, F., 2008. "The one- and multi-sample problem for functional data with application to projective shape analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 815-833, May.
  88. Chung Chang & Yakuan Chen & R. Ogden, 2014. "Functional data classification: a wavelet approach," Computational Statistics, Springer, vol. 29(6), pages 1497-1513, December.
  89. Hlubinka, Daniel & Prchal, Lubos, 2007. "Changes in atmospheric radiation from the statistical point of view," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4926-4941, June.
  90. Hervé Cardot, 2010. "Comments on: Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 30-33, May.
  91. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
  92. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  93. Ci-Ren Jiang & John A. D. Aston & Jane-Ling Wang, 2016. "A Functional Approach to Deconvolve Dynamic Neuroimaging Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 1-13, March.
  94. Leonid Torgovitski, 2015. "A Darling–Erdős-type CUSUM-procedure for functional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 1-27, January.
  95. Benko, Michal & Härdle, Wolfgang Karl & Kneip, Alois, 2006. "Common functional principal components," SFB 649 Discussion Papers 2006-010, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  96. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
  97. repec:eca:wpaper:2013/131191 is not listed on IDEAS
  98. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1047-1075, October.
  99. Boudou, Alain & Viguier-Pla, Sylvie, 2016. "Gap between orthogonal projectors—Application to stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 282-300.
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