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An introduction to recent advances in high/infinite dimensional statistics. (English) Zbl 1384.00073
From the text: The idea of this Special Issue on Statistics in High Dimensional Spaces matured during the preparation of the third edition of the International Workshop on Functional and Operatorial Statistics (IWFOS) organized in Stresa (Italy) in June 2014. While the two first editions of this event were concentrated around infinite dimensional issues, one of the main aims of the third edition was to promote links with another currently active field of statistics, namely, problems involving high (but finite) dimensional data.

MSC:
00B15 Collections of articles of miscellaneous specific interest
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
62Hxx Multivariate analysis
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[1] Ahmed, S. E., Penalty, shrinkage and pretest strategies. variable selection and estimation, (Springer Briefs in Statistics, (2014), Springer Cham) · Zbl 1306.62002
[2] Ahmedou, A.; Marion, J. M.; Pumo, B., Generalized linear model with functional predictors and their derivatives, J. Multivariate Anal., 146, 313-324, (2016) · Zbl 1337.62179
[3] Aneiros-Pérez, G.; Ferraty, F.; Vieu, P., Variable selection in partial linear regression with functional covariate, Statistics, 49, 6, 1322-1347, (2014) · Zbl 1337.62071
[4] Aneiros-Pérez, G.; Vieu, P., Semi-functional partial linear regression, Statist. Probab. Lett., 76, 11, 1102-1110, (2006) · Zbl 1090.62036
[5] Aneiros-Pérez, G.; Vieu, P., Nonparametric time series prediction: a semi-functional partial linear modelling, J. Multivariate Anal., 99, 5, 834-857, (2008) · Zbl 1133.62075
[6] Aneiros-Pérez, G.; Vieu, P., Automatic estimation procedure in partial linear model with functional data, Statist. Papers, 52, 4, 751-771, (2011) · Zbl 1229.62045
[7] Aneiros-Pérez, G.; Vieu, P., Variable selection in infinite-dimensional problems, Statist. Probab. Lett., 94, 12-20, (2014) · Zbl 1320.62163
[8] Aneiros-Pérez, G.; Vieu, P., Comments on: probability enhanced effective dimension reduction for classifying sparse functional data, Test, (2015), forthcoming
[9] Aneiros-Pérez, G.; Vieu, P., Partial linear modelling with multi-functional covariates, Comput. Statist., 30, 3, 647-671, (2014) · Zbl 1342.65016
[10] Bair, E.; Hastie, T.; Paul, D.; Tibshirani, R., Prediction by supervised principal components, J. Amer. Statist. Assoc., 101, 473, 119-137, (2006) · Zbl 1118.62326
[11] Barrientos-Marin, J.; Ferraty, F.; Vieu, P., Locally modelled regression and functional data, J. Nonparametr. Stat., 22, 5-6, 617-632, (2010) · Zbl 1327.62191
[12] Benhenni, K.; Ferraty, F.; Rachdi, M.; Vieu, P., Local smoothing regression with functional data, Comput. Statist., 22, 3, 353-369, (2007) · Zbl 1194.62042
[13] Benhenni, K.; Hedli-Griche, S.; Rachdi, M.; Vieu, P., Consistency of the regression estimator with functional data under long memory conditions, Statist. Probab. Lett., 78, 8, 1043-1049, (2008) · Zbl 1141.62314
[14] Benhenni, K.; Su, Y., Optimal sampling designs for nonparametric estimation of spatial averages of random fields, J. Multivariate Anal., 146, 341-351, (2016) · Zbl 1336.62122
[15] Berrendero, J.; Cuevas, A.; Pateiro, B., Shape classification on interpoint distance distribution, J. Multivariate Anal., 146, 237-247, (2016) · Zbl 1336.62171
[16] Berrendero, J. R.; Cuevas, A.; Torrecilla, J. L., Variable selection in functional data classification: a maxima-hunting proposal, Statist. Sinica, (2015), forthcoming · Zbl 1356.62079
[17] Biau, G.; Devroye, L.; Lugosi, G., Consistency of random forests and other averaging classifyers, J. Mach. Learn. Res., 9, 2015-2033, (2008) · Zbl 1225.62081
[18] Biau, G.; Fischer, A.; Guedj, B.; Malley, J., COBRA: A combined regression strategy, J. Multivariate Anal., 146, 18-28, (2016) · Zbl 1334.62005
[19] Blanke, D.; Bosq, D., Detecting and estimating intensity of jumps for discretely observed ARMAD(1, 1) processes, J. Multivariate Anal., 146, 119-137, (2016) · Zbl 1381.62246
[20] Bodnar, T.; Gupta, A.; Parolya, N., Direct shrinkage estimation of large dimensional precision matrix, J. Multivariate Anal., 146, 223-236, (2016) · Zbl 1338.60012
[21] E. Bongiorno, A. Goia, E. Salinelli, P. Vieu, An overview of IWFOS’2014, in: Contributions in Infinite-dimensional Statistics and Related Topics, Esculapio, Bologna, 2014, pp. 1-6.
[22] E. Bongiorno, A. Goia, E. Salinelli, P. Vieu, Contributions in infinite-dimensional statistics and related topics, Esculapio, Bologna, 2014. · Zbl 1377.62023
[23] Bosq, D., Linear processes in functional spaces, (2000), Springer-Verlag New-York · Zbl 0971.62023
[24] D. Bosq, Inférence et prévision en grandes dimensions, in: Collection Economie et Statistiques Avancées. Economica, Paris, 2005 (in French).
[25] Bosq, D.; Blanke, D., Inference and prediction in large dimensions, (Wiley Series in Probability and Statistics, (2007), John Wiley & Sons) · Zbl 1183.62157
[26] Boudou, A.; Viguier-Pla, S., Gap between orthogonal projectors. application to stationary processes, J. Multivariate Anal., 146, 282-300, (2016) · Zbl 1346.60048
[27] Bouveyron, C., Statistique en grande dimension: problématiques et enjeux, J. SFdS, 155, 2, 36-37, (2014), (French) · Zbl 1316.00032
[28] Bouveyron, C.; Brunet-Saumard, C., Model-based clustering of high-dimensional data: A review, Comput. Statist. Data Anal., 71, 52-78, (2014)
[29] Bühlmann, P.; van de Geer, S., Statistics for high-dimensional data. methods, theory and applications, (Springer Series in Statistics, (2011), Springer Heidelberg) · Zbl 1273.62015
[30] Burba, F.; Ferraty, F.; Vieu, P., K-nearest neighbour method in functional nonparametric regression, J. Nonparametr. Stat., 21, 4, 453-469, (2009) · Zbl 1161.62017
[31] Butucea, C.; Zgheib, R., Sharp minimax tests for large Toeplitz covariance matrices with repeated observations, J. Multivariate Anal., 146, 164-176, (2016) · Zbl 1334.62075
[32] Cardot, H.; Cénac, P.; Zitt, P. A., Efficient and fast estimation of the geometric Median in Hilbert spaces with an averaged stochastic gradient algorithm, Bernoulli, 19, 1, 18-43, (2013) · Zbl 1259.62068
[33] Chagny, G.; Roche, A., Adaptive estimation in the functional nonparametric regression model, J. Multivariate Anal., 146, 105-118, (2016) · Zbl 1334.62054
[34] Chen, K.; Chen, K.; Müller, H. G.; Wang, J. L., Stringing high-dimensional data for functional analysis, J. Amer. Statist. Assoc., 106, 493, 275-284, (2011) · Zbl 1396.62173
[35] Chen, D.; Hall, P.; Müller, H. G., Single and multiple index functional regression models with nonparametric link, Ann. Statist., 39, 3, 1720-1747, (2011) · Zbl 1220.62040
[36] Chiou, J. M; Yang, Y. F.; Chen, Y. T., Multivariate functional linear regression and prediction, J. Multivariate Anal., 146, 301-312, (2016) · Zbl 1336.62158
[37] Cholaquidis, A.; Fraiman, R.; Kalemkerian, J.; Llop, P., A nonlinear aggregation type classifyer, J. Multivariate Anal., 146, 269-281, (2016) · Zbl 1334.62055
[38] Chorós-Tomczyk, B.; Härdle, W.; Okhrin, O., A semi-parametric factor model for CDO surfaces dynamics, J. Multivariate Anal., 146, 151-163, (2016) · Zbl 1381.62268
[39] Collazos, J.; Dias, R.; Zambom, A., Consistent variable selection for functional regression models, J. Multivariate Anal., 146, 63-71, (2016) · Zbl 1334.62056
[40] Cuevas, A., A partial overview of the theory of statistics with functional data, J. Statist. Plann. Inference, 147, 1-23, (2014) · Zbl 1278.62012
[41] Cuevas, A.; Febero, M.; Fraiman, R., Robust estimation and classification for functional data via projection-based depth notions, Comput. Statist., 22, 481-496, (2007) · Zbl 1195.62032
[42] Daouia, A.; Gardes, L.; Girard, S., On kernel smoothing for extremal quantile regression, Bernoulli, 19, 2557-2589, (2013) · Zbl 1281.62097
[43] Debashis, P.; Aue, A., Random matrix theory in statistics: A review, J. Statist. Plann. Inference, 150, 1-29, (2014) · Zbl 1287.62011
[44] Delicado, P.; Giraldo, R.; Comas, C.; Mateu, J., Statistics for spatial functional data: some recent contributions, Environmetrics, 21, 224-239, (2010)
[45] Demongeot, J.; Hamie, A.; Laksaci, A.; Rachdi, M., Relative error prediction in nonparametric functional statistics: theory and practice, J. Multivariate Anal., 146, 261-268, (2016) · Zbl 1334.62036
[46] Febrero-Bande, M.; Galeano, P.; Gonzalez-Manteiga, W., Functional principal component regression and functional partial least squares regression: an overview and a comparative study, Int. Stat. Rev., (2015), forthcoming
[47] Ferraty, F.; Goia, A.; Salinelli, E.; Vieu, P., Functional projection pursuit regression, Test, 22, 293-320, (2013) · Zbl 1367.62117
[48] Ferraty, F.; Hall, P.; Vieu, P., Most-predictive design points for functional data predictors, Biometrika, 97, 807-824, (2010) · Zbl 1204.62064
[49] Ferraty, F.; Laksaci, A.; Tadj, A.; Vieu, P., Rate of uniform consistency for nonparametric estimates with functional variables, J. Statist. Plann. Inference, 140, 2, 335-352, (2010) · Zbl 1177.62044
[50] Ferraty, F.; Rabhi, A.; Vieu, P., Conditional quantiles for dependent functional data with application to the climatic el nino phenomenon, Sankhya, 67, 2, 378-398, (2005) · Zbl 1192.62104
[51] Ferraty, F.; Vieu, P., Nonparametric functional data analysis, (Springer Series in Statistics, (2006), Springer-Verlag New York) · Zbl 1049.62039
[52] Ferraty, F.; Vieu, P., Additive prediction and boosting for functional data, Computat. Statist. Data Anal., 53, 1400-1413, (2009) · Zbl 05687855
[53] Fraiman, R.; Gimenez, Y.; Svarc, M., Feature selection for functional data, J. Multivariate Anal., 146, 191-208, (2016) · Zbl 1335.62097
[54] Gardes, L.; Girard, S., On the estimation of the functional Weibull tail-coefficient, J. Multivariate Anal., 146, 29-45, (2016) · Zbl 1334.62094
[55] Godichon, A., Estimating the geometric Median in Hilbert spaces with stochastic gradient algorithms: \(L^p\) and almost sure rates of convergence, J. Multivariate Anal., 146, 209-222, (2016) · Zbl 1337.62053
[56] Goia, A.; Vieu, P., A partitioned single functional index model, Comput. Statist., 30, 673-692, (2014) · Zbl 1342.65034
[57] A. Goia, P. Vieu, Some advances in semiparametric functional data modelling, in: Contributions in infinite-dimensional statistics and related topics, Esculapio, Bologna, 2014, pp. 135-141.
[58] Goldenshluger, A.; Lepski, O., Bandwidth selection in kernel density estimation: oracle inequality and adaptive minimax optimality, Ann. Statist., 39, 3, 1608-1632, (2011) · Zbl 1234.62035
[59] Gonzalez-Manteiga, W.; Vieu, P., Statistics for functional data, Comput. Statist. Data Anal., 51, 10, 4788-4792, (2007) · Zbl 1162.62338
[60] Gonzalez-Manteiga, W.; Vieu, P., Methodological richness of functional data analysis, (Statistical Learning and Data Science, (2011), in: Series: Chapman & Hall/CRC Computer Science & Data Analysis)
[61] Härdle, W.; Simar, L., Applied multivariate statistical analysis, (2015), Springer Heidelberg · Zbl 1308.62002
[62] Härdle, W.; Vieu, P., Kernel regression smoothing of time series, J. Time Ser. Anal., 13, 3, 209-232, (1992) · Zbl 0759.62016
[63] Hart, J.; Vieu, P., Data-driven bandwidth choice for density estimation based on dependent data, Ann. Statist., 18, 2, 873-890, (1990) · Zbl 0703.62045
[64] Horváth, L.; Kokoszka, P., Inference for functional data with applications, (Springer Series in Statistics, (2012), Springer New York) · Zbl 1279.62017
[65] Horváth, L.; Rice, G., An introduction to functional data analysis and a principal component approach for testing the equality of mean curves, Rev. Mat. Complut., 28, 3, 505-548, (2015) · Zbl 1347.60028
[66] Hsing, T.; Eubank, R., Theoretical foundations of functional data analysis, with an introduction to linear operators, (Wiley Series in Probability and Statistics, (2015), John Wiley & Sons Chichester) · Zbl 1338.62009
[67] Huang, J.; Horowitz, J.; Wei, F., Variable selection in nonparametric additive models, Ann. Statist., 38, 4, 2282-2313, (2010) · Zbl 1202.62051
[68] Kneip, A.; Sarda, A., Factor models and variable selection in high-dimensional regression analysis, Ann. Statist., 39, 5, 2410-2447, (2011) · Zbl 1231.62131
[69] Kudraszow, N.; Vieu, P., Uniform consistency of \(k\)NN regressors for functional variables, Statist. Probab. Lett., 83, 8, 1863-1870, (2013) · Zbl 1277.62113
[70] Kuhnt, S.; Rehage, A., An angle-based multivariate functional pseudo-depth for shape outlier detection, J. Multivariate Anal., 146, 325-340, (2016) · Zbl 1381.62069
[71] Latouche, P.; Mattei, P. A.; Bouveyron, C.; Chiquet, J., Combining a relaxed EM algorithm with occam’s razor for Bayesian variable selection in high-dimensional regression, J. Multivariate Anal., 146, 177-190, (2016) · Zbl 1334.62114
[72] Lee, E.; Park, B., Sparse estimation in functional linear regression, J. Multivariate Anal., 105, 1-17, (2012) · Zbl 1236.62032
[73] Li, G.; Yang, D.; Nobel, A.; Shen, H., Supervised singular value decomposition and its asymptotic properties, J. Multivariate Anal., 146, 7-17, (2016) · Zbl 1336.62129
[74] Lian, H., Functional partial linear model, J. Nonparametr. Stat., 23, 1, 115-128, (2011) · Zbl 1359.62157
[75] Ling, N.; Liang, L.; Vieu, P., Nonparametric regression estimation for functional stationary ergodic data with missing at random, J. Statist. Plann., 162, 75-87, (2015) · Zbl 1314.62102
[76] McKeague, I.; Sen, B., Fractals with point impact in functional linear regression, Ann. Statist., 38, 4, 2559-2586, (2010) · Zbl 1196.62116
[77] Meier, L.; van de Geer, S.; Bühlmann, P., High-dimensional additive modelling, Ann. Statist., 37, 6, 3779-3821, (2009) · Zbl 1360.62186
[78] Menafoglio, A.; Petris, G., Kriging for Hilbert-space valued random fields: the operatorial point of view, J. Multivariate Anal., 146, 84-94, (2016) · Zbl 1337.60103
[79] Müller, H. G., Functional modelling and classification of longitudinal data, Scand. J. Stat., 3, 223-240, (2005) · Zbl 1089.62072
[80] Müller, H. G.; Yao, F., Functional additive models, J. Amer. Statist. Assoc., 103, 1534-1544, (2005) · Zbl 1286.62040
[81] Nagy, S.; Gijbels, I.; Hublinka, D., Weak convergence of discretely observed functional data with applications, J. Multivariate Anal., 146, 46-62, (2016) · Zbl 1334.62090
[82] O’Hara, R.; Sillanpää, M., A review of Bayesian variable selection methods: what, how and which, Bayesian Anal., 4, 85-117, (2009) · Zbl 1330.62291
[83] Rachdi, M.; Vieu, P., Nonparametric regression for functional data: automatic smoothing parameter selection, J. Statist. Plann. Inference, 137, 9, 2784-2801, (2007) · Zbl 1331.62240
[84] Ramsay, J.; Silverman, B., Applied functional data analysis. methods and case studies, (Springer Series in Statistics, (2002), Springer New York) · Zbl 1011.62002
[85] Ramsay, J.; Silverman, B., (Springer Series in Statistics, (2005), Springer New York)
[86] Ruiz-Medina, M. D.; Romano, E.; Fernandez-Pascual, R., Plug-in prediction intervals for a special case of standard ARH(1) processes, J. Multivariate Anal., 146, 138-150, (2016) · Zbl 1346.60052
[87] Scheipl, F.; Staicu, A. M.; Greven, S., Functional additive mixed models, J. Comput. Graph. Statist., 24, 2, 477-501, (2015)
[88] Scornet, E., On the asymptotics of random forests, J. Multivariate Anal., 146, 72-83, (2016) · Zbl 1337.62063
[89] Shang, H. L., A Bayesian approach for determining the optimal semi-metric and bandwidth in scalar-on-function quantile regression with unknown error density and dependent functional data, J. Multivariate Anal., 146, 95-104, (2016) · Zbl 1335.62079
[90] Sorensen, H.; Goldsmith, J.; Sangalli, L., An introduction with medical applications to functional data analysis, Stat. Med., 32, 30, 5222-5240, (2013)
[91] Tibshirani, R., Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B, 58, 267-288, (1996) · Zbl 0850.62538
[92] Valderrama, M., An overview to modelling functional data, Comput. Statist., 22, 3, 331-334, (2007)
[93] van de Geer, S., High-dimensional generalized linear models and the lasso, Ann. Statist., 36, 614-645, (2008) · Zbl 1138.62323
[94] van de Geer, S., Worst possible sub-directions in high dimensional models, J. Multivariate Anal., 146, 248-260, (2016) · Zbl 1334.62133
[95] Zhang, J., Analysis of variance for functional data, (2013), in: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
[96] Zhao, Y.; Todd, O.; Reiss, P., Wavelet-based LASSO in functional linear regression, J. Comput. Graph. Statist., 21, 3, 600-617, (2012)
[97] Zhaoping, H.; Heng, L., Genetic networks from time course expression data using functional regression with lasso penalty, Comm. Statist. Theory Methods, 40, 10, 1768-1779, (2011) · Zbl 1216.62170
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