Adaptive slicing for functional slice inverse regression. (English) Zbl 07889358
Summary: In the paper, we propose a functional dimension reduction method for functional predictors and a scalar response. In the past study, the most popular functional dimension reduction method is the functional sliced inverse regression (FSIR) and people usually use a fixed slicing scheme to implement the estimation of FSIR. However, in practical, there are two main questions for the fixed slicing scheme: how many slices should be chosen and how to divide all samples into different slices. To solve these problems, we first expand the functional predictor and functional regression parameters on the functional principal component basis or a given basis such as B-spline basis. Then the functional regression parameters will be estimated by using the adaptive slicing for FSIR approach. Simulation results and real data analysis are presented to show the merit of the new proposed method.
MSC:
| 62-XX | Statistics |
Software:
fda (R)References:
| [1] | AitSaïdi, A.; Ferraty, F.; Kassa, R.; Vieu, P., Cross-validated estimations in the single-functional index model, Statistics, 42, 475-494, 2008 · Zbl 1274.62519 · doi:10.1080/02331880801980377 |
| [2] | Amato, U.; Antoniadis, A.; Feis, ID, Dimension reduction in functional regression with applications, Comput Stat Data Anal, 50, 2422-2446, 2006 · Zbl 1445.62078 · doi:10.1016/j.csda.2004.12.007 |
| [3] | Bongiorno, EG; Salinelli, E.; Goia, A.; Vieu, P., Contributions in infinite-dimensional statistics and related topics, 2014, Bologna: Società Editrice Esculapio, Bologna · Zbl 1377.62023 · doi:10.15651/9788874887637 |
| [4] | Borggaard, C.; Thodberg, HH, Optimal minimal neural interpretation of spectra, Anal Chem, 64, 545-551, 1992 · doi:10.1021/ac00029a018 |
| [5] | Cardot, H.; Ferraty, F.; Sarda, P., Spline estimators for the functional linear model, Stat Sin, 13, 571-591, 2003 · Zbl 1050.62041 |
| [6] | Du, J.; Sun, XQ; Cao, RY; Zhang, ZZ, Statistical inference for partially linear additive spatial autoregressive models, Spatial Stat, 25, 52-67, 2018 · doi:10.1016/j.spasta.2018.04.008 |
| [7] | Ferraty, F.; Vieu, P., Nonparametric functional data analysis: theory and practice, 2006, New York: Springer, New York · Zbl 1119.62046 |
| [8] | Ferraty, F.; Mas, A.; Vieu, P., Nonparametric regression on functional data: inference and practical aspects, Aust N Z J Stat, 49, 267-286, 2007 · Zbl 1136.62031 · doi:10.1111/j.1467-842X.2007.00480.x |
| [9] | Ferré, L.; Yao, AF, Functional sliced inverse regression analysis, Statistics, 37, 475-488, 2003 · Zbl 1032.62052 · doi:10.1080/0233188031000112845 |
| [10] | Ferré, L.; Yao, AF, Smoothed functional inverse regression, Stat Sin, 15, 665-683, 2005 · Zbl 1086.62054 |
| [11] | Gramacy, RB; Lee, HKH, Bayesian treed Gaussian process models with an application to computer modeling, J Am Stat Assoc, 103, 1119-1130, 2008 · Zbl 1205.62218 · doi:10.1198/016214508000000689 |
| [12] | He, G.; Müller, HG; Wang, JL, Functional canonical analysis for square integrable stochastic processes, J Multivar Anal, 85, 54-77, 2003 · Zbl 1014.62070 · doi:10.1016/S0047-259X(02)00056-8 |
| [13] | Horváth, L.; Kokoszka, P., Inference for functional data with applications, 2012, New York: Springer, New York · Zbl 1279.62017 · doi:10.1007/978-1-4614-3655-3 |
| [14] | Hu WJ, Guo JX, Wang GC, Zhang BX (2020) Weight fused functional sliced average variance estimation. Commun Stat-Simul Comput, pp 1-9 |
| [15] | James, G.; Hastie, T.; Sugar, C., Principal component models for sparse functional data, Biomatrika, 87, 587-602, 2000 · Zbl 0962.62056 · doi:10.1093/biomet/87.3.587 |
| [16] | Li, KC, Sliced inverse regression for dimension reduction, J Am Stat Assoc, 86, 316-327, 1991 · Zbl 0742.62044 · doi:10.1080/01621459.1991.10475035 |
| [17] | Li, B.; Zha, HY; Chiaromonte, F., Contour regression: a general approach to dimension reduction, Ann Stat, 33, 1580-1616, 2005 · Zbl 1078.62033 · doi:10.1214/009053605000000192 |
| [18] | Lian, H.; Li, GR, Series expansion for functional sufficient dimension reduction, J Multivar Anal, 124, 150-165, 2014 · Zbl 1278.62055 · doi:10.1016/j.jmva.2013.10.019 |
| [19] | Liang, BT; Gao, TX; Bai, DF; Wang, GC, Functional dimension reduction based on fuzzy partition and transformation, Aust N Z J Stat, 64, 45-66, 2021 · Zbl 1521.62056 · doi:10.1111/anzs.12363 |
| [20] | Ramsay, JO; Silverman, BW, Applied functional data analysis: methods and case studies, 2002, New York: Springer, New York · Zbl 1011.62002 · doi:10.1007/b98886 |
| [21] | Ramsay, JO; Silverman, BW, Functional data analysis, 2005, New York: Springer, New York · Zbl 1079.62006 · doi:10.1007/b98888 |
| [22] | Wang, T., Dimension reduction via adaptive slicing, Stat Sin, 32, 499-516, 2022 · Zbl 1524.62194 |
| [23] | Wang, GC; Lian, H., Functional sliced inverse regression in a reproducing Kernel Hilbert space: a theoretical connection to functional linear regression, Stat Sin, 30, 17-33, 2020 · Zbl 1444.62169 |
| [24] | Wang, GC; Lin, N.; Zhang, BX, Functional contour regression, J Multivar Anal, 11, 1-13, 2013 · Zbl 1277.62119 · doi:10.1016/j.jmva.2012.11.005 |
| [25] | Wang, GC; Lin, N.; Zhang, BX, Functional k-means inverse regression, Comput Stat Data Anal, 70, 172-182, 2014 · Zbl 1471.62207 · doi:10.1016/j.csda.2013.09.004 |
| [26] | Wang, GC; Zhou, Y.; Feng, XN; Zhang, BX, The hybrid method of FSIR and FSAVE for functional effective dimension reduction, Comput Stat Data Anal, 91, 64-77, 2015 · Zbl 1468.62205 · doi:10.1016/j.csda.2015.05.011 |
| [27] | Wang, GC; Feng, XN; Chen, M., Functional partial linear single-index model, Scand J Stat, 43, 261-274, 2016 · Zbl 1371.62037 · doi:10.1111/sjos.12178 |
| [28] | Wang, GC; Zhou, JJ; Wu, WQ; Chen, M., Robust functional sliced inverse regression, Stat Pap, 58, 227-245, 2017 · Zbl 1394.62049 · doi:10.1007/s00362-015-0695-x |
| [29] | Wang, GC; Zhang, BX; Liao, WH; Xie, BJ, Estimation of functional regression model via functional dimension reduction, J Comput Appl Math, 379, 1-19, 2020 · Zbl 1440.62406 · doi:10.1016/j.cam.2020.112948 |
| [30] | Yao, F.; Müller, HG, Functional quadratic regression, Biomatrika, 97, 49-64, 2010 · Zbl 1183.62113 · doi:10.1093/biomet/asp069 |
| [31] | Yao, F.; Müller, HG; Wang, JL, Functional data analysis for sparse longitudinal data, J Am Stat Assoc, 100, 577-590, 2005 · Zbl 1117.62451 · doi:10.1198/016214504000001745 |
| [32] | Yao, F.; Lei, E.; Wu, Y., Effective dimension reduction for sparse functional data, Biomatrika, 102, 421-437, 2015 · Zbl 1452.62996 · doi:10.1093/biomet/asv006 |
| [33] | Yu, P.; Du, J.; Zhang, Z., Varying-coefficient partially functional linear quantile regression models, J Korean Stat Soc, 46, 462-475, 2017 · Zbl 1368.62104 · doi:10.1016/j.jkss.2017.02.001 |
| [34] | Zhang, JT; Chen, J., Statistical inferences for functional data, Ann Stat, 35, 1052-1079, 2007 · Zbl 1129.62029 · doi:10.1214/009053606000001505 |
| [35] | Zhou, J.; Chen, Z.; Peng, Q., Polynomial spline estimation for partial functional linear regression models, Comput Stat, 31, 1107-1129, 2016 · Zbl 1347.65036 · doi:10.1007/s00180-015-0636-0 |
| [36] | Zipunnikov, V.; Caffo, B.; Yousem, DM; Davatzikos, C.; Schwartz, BS; Crainiceanu, C., Multilevel functional principal component analysis for high-dimensional data, J Comput Gr Stat, 20, 852-873, 2011 · doi:10.1198/jcgs.2011.10122 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
