广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (1): 15-29.doi: 10.16088/j.issn.1001-6600.2021060908

• 综述 • 上一篇    下一篇

函数型数据广义线性模型和分类问题综述

白德发1, 徐欣2, 王国长2*   

  1. 1.暨南大学 地方研究总院, 广东 广州 510632;
    2.暨南大学 经济学院, 广东 广州 510632
  • 收稿日期:2021-06-09 修回日期:2021-06-28 出版日期:2022-01-25 发布日期:2022-01-24
  • 通讯作者: 王国长(1983—), 男, 湖南祁东人, 暨南大学副教授, 博士。E-mail: twanggc@jnu.edu.cn
  • 基金资助:
    国家社会科学基金(20BTJ041)

Review of Generalized Linear Models and Classification for Functional Data

BAI Defa1, XU Xin2, WANG Guochang2*   

  1. 1. Office of Scientific R & D, Jinan University, Guangzhou Guangdong 510632, China;
    2. College of Economics, Jinan University, Guangzhou Guangdong 510632, China
  • Received:2021-06-09 Revised:2021-06-28 Online:2022-01-25 Published:2022-01-24

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摘要： 函数型数据采用全非参数的方法,假设数据来自一条光滑的曲线,把整个曲线当成一个样本来处理,从而避免高维和高度相关的问题。其研究始于20世纪50年代,经过近70多年来的发展,很多经典的统计分析方法都被推广到函数型数据,且被中外学者写成综述和相关书籍以便研究者使用,如主成分、典型相关、线性模型和聚类问题等。但是,目前仍缺少有关函数广义线性模型和分类问题的综述和书籍。基于此,本文从函数型数据发展的数据形式、函数近似包括基底展开和主成分、函数广义线性模型和分类等问题的发展历程及未来发展方向等方面进行详细的综述。进一步,为了能够在经济、金融、医学、气象和环境等领域更好地应用函数型数据,本文提供了具体的样条估计计算程序。

关键词: 函数型数据, 广义线性模型, 分类, 函数主成分分析, 函数线性模型

Abstract: The all non-parametric method suppose that functional data comes from a smooth curve. The whole curve is treated as a sample to avoid the problems of high dimension and high correlation. The research of functional data began in 1950s. After more than 100 years of development, many classical statistical analysis methods have been extended to functional data, and written in review and related books by Chinese and foreign scholars for other researchers to use, such as principal component, typical correlation, linear model and clustering problems. However, there are few books and reviews about generalized linear models and classification for functional data. This article gives a detailed review of the development process and future development directions of the functional data analysis and the function approximation, including the basis expansion and principal components, the generalized linear model and classification of functional data. Furthermore, in order to better apply functional data in the fields of economy, finance, medicine, meteorology and environment, some specific calculation programs for the B-spline are provided in this article.

Key words: functional data, generalized linear models, classification, functional principal component analysis, functional linear model

中图分类号: 

  • O212.7
[1] JAMES G M, HASTIE T J. Functional linear discriminant analysis for irregularly sampled curves[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2001, 63(3): 533-550.
[2]SILVERMAN B W. Smoothed functional principal components analysis by choice of norm[J]. The Annals of Statistics, 1996, 24(1): 1-24.
[3]RAMSAY J O, DALZELL C J. Some tools for functional data analysis[J]. Journal of the Royal Statistical Society, Series B (Methodological), 1991, 53(3): 539-561.
[4]GRENANDER U. Stochastic processes and statistical inference[J]. Arkiv för Matematik, 1950, 1(3): 195-277.
[5]RAO C R. Some statistical methods for comparison of growth curves[J]. Biometrics, 1958, 14(1): 1-17.
[6]ZIPUNNIKOV V, GREVEN S, SHOU H C, et al. Longitudinal high-dimensional principal components analysis with application to diffusion tensor imaging of multiple sclerosis[J]. The Annals of Applied Statistics, 2014, 8(4): 2175-2202.
[7]XIAO L, ZIPUNNIKOV V, RUPPERT D, et al. Fast covariance estimation for high-dimensional functional data[J]. Statistics and Computing, 2016, 26: 409-421.
[8]王德青,朱建平,刘晓葳,等.函数型数据聚类分析研究综述与展望[J].数理统计与管理,2018,37(1):51-63.
[9]XUE K J, YAO F. Distribution and correlation-free two-sample test of high-dimensional means[J]. The Annals of Statistics, 2020, 48(3): 1304-1328.
[10]RAMSAY J O, SILVERMAN B W. Functional data analysis[M]. New York: Springer, 2005: 147-172.
[11]RAMSAY J, HOOKER G, GRAVES S. Functional data analysis with R and MATLAB[M]. New York: Springer, 2009: 1-2.
[12]FERRATY F, VIEU P. Nonparametric functional data analysis: theory and practice[M]. New York: Springer, 2006.
[13]HALL P, YANG Y J. Ordering and selecting components in multivariate or functional data linear prediction[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2010, 72(1): 93-110.
[14]DELAIGLE A, HALL P. Achieving near perfect classification for functional data[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2012, 74(2): 267-286.
[15]YUAN M, CAI T T. A reproducing kernel Hilbert space approach to functional linear regression[J]. The Annals of Statistics, 2010, 38(6): 3412-3444.
[16]CAI T T, HALL P. Prediction in functional linear regression[J]. The Annals of Statistics, 2006, 34(5): 2159-2179.
[17]CAI T T, YUAN M. Adaptive covariance matrix estimation through block thresholding[J]. The Annals of Statistics, 2012, 40(4): 2014-2042.
[18]CHIOU J M, MÜLLER H G, WANG J L, et al. A functional multiplicative effects model for longitudinal data, with application to reproductive histories of female medflies[J]. Statistica Sinica, 2003, 13(4): 1119-1133.
[19]CHIOU J M, MÜLLER H G, WANG J L. Functional quasi-likelihood regression models with smooth random effects[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2003, 65(2): 405-423.
[20]YAO F, MÜLLER H G, WANG J L. Functional linear regression analysis for longitudinal data[J]. The Annals of Statistics, 2005, 33(6): 2873-2903.
[21]YAO F, MÜLLER H G. Functional quadratic regression[J]. Biometrika, 2010, 97(1): 49-64.
[22]HE G, MÜLLER H G, WANG J L, et al. Functional linear regression via canonical analysis[J]. Bernoulli, 2010, 16(3): 705-729.
[23]ŞENTÜRK D. MÜLLER H G. Functional varying coefficient models for longitudinal data[J]. Journal of the American Statistical Association, 2010, 105(491): 1256-1264.
[24]MÜLLER H G, YAO F. Additive modelling of functional gradients[J]. Biometrika, 2010, 97(4): 791-805.
[25]WANG J L, CHIOU J M, MÜLLER H G. Functional data analysis[J]. Annual Review of Statistics and Its Application, 2016, 3: 257-295.
[26]ASH R B, GARDNER M F. Topics in stochastic processes[J]. Bulletin of the American Mathematical Society, 1976, 82: 817-820.
[27]HORVÁTH L, KOKOSZKA P. Inference for functional data with applications[M]. New York: Springer, 2012.
[28]ZHANG H Z, WANG F Q, CHEN Y, et al. Sample pair based sparse representation classification for face recognition[J]. Expert Systems with Applications, 2016, 45: 352-358.
[29]DAI X T, MÜLLER H G. Principal component analysis for functional data on Riemannian manifolds and spheres[J]. The Annals of Statistics, 2018, 46(6B): 3334-3361.
[30]LIN Z H, YAO F. Intrinsic Riemannian functional data analysis[J]. The Annals of Statistics, 2019, 47(6): 3533-3577.
[31]LIN T Y, FAN C Y, HO N, et al. Projection robust Wasserstein distance and Riemannian optimization[C]//34th Conference on Neural Information Processing Systems (NeurIPS 2020). Vancouver: NeurIPS, 2020: 1-15.
[32]ZHU H T, FAN J Q, KONG L L. Spatially varying coefficient model for neuroimaging data with jump discontinuities[J]. Journal of the American Statistical Association, 2014, 109(507): 1084-1098.
[33]GOLDSMITH J, HUANG L, CRAINICEANU C M. Smooth scalar-on-image regression via spatial Bayesian variable selection[J]. Journal of Computational and Graphical Statistics, 2014, 23(1): 46-64.
[34]WANG X J, NAN B, ZHU J, et al. Regularized 3D functional regression for brain image data via Haar wavelets[J]. The Annals of Applied Statistics, 2014, 8(2): 1045-1064.
[35]YAO F, MÜLLER H G, WANG J L. Functional data analysis for sparse longitudinal data[J]. Journal of the American Statistical Association, 2005, 100(470): 577-590.
[36]PENG J, PAUL D. A geometric approach to maximum likelihood estimation of the functional principal components from sparse longitudinal data[J]. Journal of Computational and Graphical Statistics, 2009, 18(4): 995-1015.
[37]CHEN K H, LEI J. Localized functional principal component analysis[J]. Journal of the American Statistical Association, 2015, 110(511): 1266-1275.
[38]LEURGANS S E, MOYEED R A, SILVERMAN B W. Canonical correlation analysis when the data are curves[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1993, 55(3): 725-740.
[39]HE G Z, MÜLLER H G, WANG J L. Functional canonical analysis for square integrable stochastic processes[J]. Journal of Multivariate Analysis, 2003, 85(1): 54-77.
[40]HE G Z, MÜLLER H G, WANG J L. Methods of canonical analysis for functional data[J]. Journal of Statistical Planning and Inference, 2004, 122(1/2): 141-159.
[41]CARDOT H, FERRATY F, SARDA P. Functional linear model[J]. Statistics & Probability Letters, 1999, 45(1): 11-22.
[42]CARDOT H, FERRATY F, SARDA P. Spline estimators for the functional linear model[J]. Statistica Sinica, 2003, 13(3): 571-591.
[43]MÜLLER H G, YAO F. Functional additive models[J]. Journal of the American Statistical Association, 2008, 103(484): 1534-1544.
[44]WANG Q, YIN X R. Aggregate inverse mean estimation for sufficient dimension reduction[J]. Technometrics, 2021, 63(4): 456-465.
[45]FARAWAY J J. Regression analysis for a functional response[J]. Technometrics, 1997, 39(3): 254-261.
[46]SHEN Q, FARAWAY J. An F test for linear models with functional responses[J]. Statistica Sinica, 2004, 14(4): 1239-1257.
[47]YANG Y H. Consistency of cross validation for comparing regression procedures[J]. The Annals of Statistics, 2007, 35(6): 2450-2473.
[48]FAN J, ZHANG J T. Two-step estimation of functional linear models with applications to longitudinal data[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2000, 62(2): 303-322.
[49]FERRATY F, MAS A, VIEU P. Nonparametric regression on functional data: inference and practical aspects[J]. Australian & New Zealand Journal of Statistics, 2007, 49(3): 267-286.
[50]JAMES G M, SILVERMAN B W. Functional adaptive model estimation[J]. Journal of the American Statistical Association, 2005, 100(470): 565-576.
[51]CHEN D, HALL P, MÜLLER H G. Single and multiple index functional regression models with nonparametric link[J]. The Annals of Statistics, 2011, 39(3): 1720-1747.
[52]AIT-SAïDI A, FERRATY F, KASSA R, et al. Cross-validated estimations in the single-functional index model[J]. Statistics, 2008, 42(6): 475-494.
[53]WANG Q, XUE Y. An ensemble of inverse moment estimators for sufficient dimension reduction[J]. Computational Statistics & Data Analysis, 2021, 161: 107241.
[54]WANG G C, LIAN H. Functional sliced inverse regression in a reproducing kernel Hilbert space: a theoretical connection to functional linear regression[J]. Statistica Sinica, 2020, 30: 17-33.
[55]WANG G C, LIN N, ZHANG B X. Functional contour regression[J]. Journal of Multivariate Analysis, 2013, 116: 1-13.
[56]LIAN H. Shrinkage estimation and selection for multiple functional regression[J]. Statistica Sinica, 2013, 23(1): 51-74.
[57]FERRÉ L, YAO A F. Smoothed functional inverse regression[J]. Statistica Sinica, 2005, 15(3): 665-683.
[58]FERRÉ L, YAO A F. Functional sliced inverse regression analysis[J]. Statistics, 2003, 37(6): 475-488.
[59]DU J, SUN X Q, CAO R Y, et al. Statistical inference for partially linear additive spatial autoregressive models[J]. Spatial Statistics, 2018, 25: 52-67.
[60]YU P, DU J, ZHANG Z Z. Varying-coefficient partially functional linear quantile regression models[J]. Journal of the Korean Statistical Society, 2017, 46(3): 462-475.
[61]KONG D H, STAICU A M, MAITY A. Classical testing in functional linear models[J]. Journal of Nonparametric Statistics, 2016, 28(4): 813-838.
[62]ZHOU J J, CHEN M. Spline estimators for semi-functional linear model[J]. Statistics & Probability Letters, 2012, 82(3): 505-513.
[63]BOSQ D. Linear processes in function spaces: theory and applications[M]. New York: Springer, 2000: 127-145.
[64]HÖRMANN S, HORVÁTH L, REEDER R. A functional version of the ARCH model[J]. Econometric Theory, 2013, 29(2): 267-288.
[65]ENGLE R F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica, 1982, 50(4): 987-1007.
[66]AUE A, HORVÁTH L, PELLATT D F. Functional generalized autoregressive conditional heteroskedasticity[J]. Journal of Time Series Analysis, 2017, 38(1): 3-21.
[67]BOLLERSLEV T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31(3): 307-327.
[68]MÜLLER H G, SEN R, STADTMÜLLER U. Functional data analysis for volatility[J]. Journal of Econometrics, 2011, 165(2): 233-245.
[69]HORVÁTH L, KOKOSZKA P, RICE G. Testing stationarity of functional time series[J]. Journal of Econometrics, 2014, 179(1): 66-82.
[70]KOKOSZKA P, MIAO H, REIMHERR M, et al. Dynamic functional regression with application to the cross-section of returns[J]. Journal of Financial Econometrics, 2018, 16(3): 461-485.
[71]DETTE H, KOKOT K, VOLGUSHEV S. Testing relevant hypotheses in functional time series via self-normalization[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2020, 82(3): 629-660.
[72]李因果,戴翼,何晓群.基于自适应权重的面板数据聚类方法[J].系统工程理论与实践,2013,33(2):388-395.
[73]朱建平,陈民恳.面板数据的聚类分析及其应用[J].统计研究,2007,24(4):11-14.
[74]李因果,何晓群.面板数据聚类方法及应用[J].统计研究,2010,27(9):73-79.
[75]王德青,朱建平,王洁丹.基于自适应权重的函数型数据聚类方法研究[J].数理统计与管理,2015,34(1):84-92.
[76]王德青,刘晓葳,朱建平.函数型自适应权重聚类分析的再拓展[J].数理统计与管理,2016,35(1):81-88.
[77]王劼,黄可飞,王惠文.一种函数型数据的聚类分析方法[J].数理统计与管理,2009,28(5):839-844.
[78]CHIOU J M, LI P L. Correlation-based functional clustering via subspace projection[J]. Journal of the American Statistical Association, 2008, 103(484): 1684-1692.
[79]GARCIA-ESCUDERO L A. GORDALIZA A. A proposal for robust curve clustering[J]. Journal of Classification, 2005, 22(2): 185-201.
[80]SERBAN N, WASSERMAN L. CATS: clustering after transformation and smoothing[J]. Journal of the American Statistical Association, 2005, 100(471): 990-999.
[81]CHIOU J M, LI P L. Functional clustering and identifying substructures of longitudinal data[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2007, 69(4): 679-699.
[82]ABRAHAM C, CORNILLON P A, MATZNER-LØBER E, et al. Unsupervised curve clustering using B-splines[J]. Scandinavian Journal of Statistics, 2003, 30(3): 581-595.
[83]HECKMAN N E, ZAMAR R H. Comparing the shapes of regression functions[J]. Biometrika, 2000, 87(1): 135-144.
[84]TARPEY T, KINATEDER K K J. Clustering functional data[J]. Journal of Classification, 2003, 20(1): 93-114.
[85]靳刘蕊.基于变化趋势相异性的金融时间序列函数聚类分析[J].经济经纬,2010(2):66-69.
[86]IEVA F, PAGANONI A M, PIGOLI D, et al. Multivariate functional clustering for the morphological analysis of electrocardiograph curves[J]. Journal of the Royal Statistical Society Series C-Applied Statistics, 2013, 62(3): 401-418.
[87]DELAIGLE A, HALL P. Defining probability density for a distribution of random functions[J]. The Annals of Statistics, 2010, 38(2): 1171-1193.
[88]HEARD N A, HOLMES C C, STEPHENS D A. A quantitative study of gene regulation involved in the immune response of Anopheline mosquitoes: an application of Bayesian hierarchical clustering of curves[J]. Journal of the American Statistical Association, 2006, 101(473): 18-29.
[89]PETERSEN A, MÜLLER H G. Functional data analysis for density functions by transformation to a Hilbert space[J]. The Annals of Statistics, 2016, 44(1): 183-218.
[90]RAMSAY J O, RAMSEY J B. Functional data analysis of the dynamics of the monthly index of nondurable goods production[J]. Journal of Econometrics, 2002, 107(1/2): 327-344.
[91]FERRATY F, LAKSACI A, TADJ A, et al. Rate of uniform consistency for nonparametric estimates with functional variables[J]. Journal of Statistical Planning and Inference, 2010, 140(2): 335-352.
[92]JAMES G M. Generalized linear models with functional predictors[J]. Journal of the Royal Statistical Society Series B-Statistical Methodology, 2002, 64(3): 411-432.
[93]ESCABIAS M, AGUILERA A M, VALDERRAMA M J. Principal component estimation of functional logistic regression: discussion of two different approaches[J]. Journal of Nonparametric Statistics, 2004, 16(3/4): 365-384.
[94]CARDOT H, SARDA P. Estimation in generalized linear models for functional data via penalized likelihood[J]. Journal of Multivariate Analysis, 2005, 92(1): 24-41.
[95]MÜLLER H G, STADTMÜLLER U. Generalized functional linear models[J]. The Annals of Statistics, 2005, 33(2): 774-805.
[96]ESCABIAS M, AGUILERA A M, VALDERRAMA M J. Modeling environmental data by functional principal component logistic regression[J]. Environmetrics, 2005, 16(1): 95-107.
[97]ESCABIAS M, AGUILERA A M, VALDERRAMA M J. Functional PLS logit regression model[J]. Computational Statistics & Data Analysis, 2007, 51(10): 4891-4902.
[98]AGUILERA A M, ESCABIAS M, VALDERRAMA M J. Discussion of different logistic models with functional data. Application to systemic lupus erythematosus[J]. Computational Statistics & Data Analysis, 2008, 53(1): 151-163.
[99]ZHU H X. A functional generalized linear model with curve selection in cervical pre-cancer diagnosis using Fluorescence spectroscopy[C]// Institute of Mathematical Statistics. Institute of Mathematical Statistics lecture notes:monograph series. Beachwood: Institute of Mathematical Statistics, 2009: 173-189.
[100]GERTHEISS J, MAITY A, STAICU A M. Variable selection in generalized functional linear models[J]. Stat, 2013, 2(1): 86-101.
[101]MCLEAN M W, HOOKER G, STAICU A M, et al. Functional generalized additive models[J]. Journal of Computational and Graphical Statistics, 2014, 23(1): 249-269.
[102]MATSUI H. Variable and boundary selection for functional data via multiclass logistic regression modeling[J]. Computational Statistics & Data Analysis, 2014, 78: 176-185.
[103]FAN R Z, WANG Y F, MILLS J L, et al. Generalized functional linear models for gene-based case-control association studies[J]. Genetic Epidemiology, 2014, 38(7): 622-637.
[104]SHANG Z F, CHENG G. Nonparametric inference in generalized functional linear models[J]. The Annals of Statistics, 2015, 43(4): 1742-1773.
[105]FAN R Z, WANG Y F, BOEHNKE M, et al. Gene level meta-analysis of quantitative traits by functional linear models[J]. Genetics, 2015, 200(4): 1089-1104.
[106]JADHAV S, KOUL H L, LU Q. Miscellanea dependent generalized functional linear models[J]. Biometrika, 2017, 104(4): 987-994.
[107]SCHEFFLER A W, TELESCA D, SUGAR C A, et al. Covariate-adjusted region-referenced generalized functional linear model for EEG data[J]. Statistics in Medicine, 2019, 38(30): 5587-5602.
[108]ZHANG H L, ZOU G H. Cross-validation model averaging for generalized functional linear model[J]. Econometrics, 2020, 8(1): 7.
[109]STONE C J. Consistent nonparametric regression[J]. The Annals of Statistics, 1977, 5(4): 595-620.
[110]DEVROYE L, LUGOSI G. A universally acceptable smoothing factor for kernel density estimates[J]. The Annals of Statistics, 1996, 24(6): 2499-2512.
[111]FERRATY F, VIEU P. Curves discrimination: a nonparametric functional approach[J]. Computational Statistics & Data Analysis, 2003, 44(1/2): 161-173.
[112]BIAU G, BUNEA F, WEGKAMP M H. Functional classification in Hilbert spaces[J]. IEEE Transactions on Information Theory, 2005, 51(6): 2163-2172.
[113]LENG X Y, MÜLLER H G. Classification using functional data analysis for temporal gene expression data[J]. Bioinformatics, 2006, 22(1): 68-76.
[114]ABRAHAM C, BIAU G, CADRE B. On the kernel rule for function classification[J]. Annals of the Institute of Statistical Mathematics, 2006, 58(3): 619-633.
[115]ROSSI F, VILLA N. Support vector machine for functional data classification[J]. Neurocomputing, 2006, 69(7/9): 730-742.
[116]WANG X H, RAY S, MALLICK B K. Bayesian curve classification using wavelets[J]. Journal of the American Statistical Association, 2007, 102(479): 962-973.
[117]PREDA C, SAPORTA G, LÉVÉDER C. PLS classification of functional data[J]. Computational Statistics, 2007, 22(2): 223-235.
[118]GOMEZ-VERDEJO V, ARENAS-GARCIA J, FIGUEIRAS-VIDAL A R. A dynamically adjusted mixed emphasis method for building boosting ensembles[J]. IEEE Transactions on Neural Networks, 2008, 19(1): 3-17.
[119]ROSSI F, VILLA N. Recent advances in the use of SVM for functional data classification[C]//Functional and Operatorial Statistics. Heidelberg: Physica-Verlag HD, 2008: 273-280.
[120]LI B, YU Q. Classification of functional data: a segmentation approach[J]. Computational Statistics & Data Analysis, 2008, 52(10): 4790-4800.
[121]BERLINET A, BIAU G, ROUVIERE L. Functional supervised classification with wavelets[J]. Annales de l’ISUP, 2008, 52(21):61-80.
[122]RABAOUI A, KADRI H, DAVY M. Nonparametric Bayesian supervised classification of functional data[C]//2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Kyoto: IEEE, 2012: 3381-3384.
[123]CHANG C, CHEN Y K, OGDEN R T. Functional data classification: a wavelet approach[J]. Computational Statistics, 2014, 29(6): 1497-1513.
[124]BERRENDERO J R, CUEVAS A, TORRECILLA J L. Variable selection in functional data classification: a maxima-hunting proposal[J]. Statistica Sinica, 2016, 26(2): 619-638.
[125]DARABI N, HOSSEINI-NASAB S M E. Projection-based classification for functional data[J]. Statistics, 2020, 54(3): 544-558.
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