JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (3): 100-106.doi: 10.6040/j.issn.1671-9352.0.2024.051

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Partially functional linear quantile regression model and its application for incomplete observations

YANG Yujie, LING Nengxiang*   

  1. School of Mathematics, Hefei University of Technology, Hefei 230009, Anhui, China
  • Published:2025-03-10

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Abstract: Firstly, based on incomplete observed functional data, partially functional linear quantile regression model, the estimation method and prediction step are introduced. Secondly, due to the widespread existence of incomplete observed functional variables, the mast records every 10 minutes from April 8, 2019 to August 31, 2020 in Nepal for empirical analysis are used. Aiming at the incomplete functional characteristics of wind speed data, an incomplete partial functional linear quantile regression model with daily mean air pressure as the response variable is constructed, and the estimators of the unknown slope function and unknown parameters of the model are obtained, and the daily mean air pressure is predicted and analyzed, which further illustrates the effectiveness of the model and the method.

Key words: functional data analysis, incomplete observation, partial linear quantile regression, principal component analysis

CLC Number: 

  • O212.7
[1] RAMSAY J, SILVERMAN B. Functional data analysis[M]. New York: Springer, 2005.
[2] FERRATY F, VIEU P. Nonparametric functional data analysis:theory and practice[M]. New York: Springer, 2006.
[3] HALL P, HOROWITZ J L. Methodology and convergence rates for functional linear regression[J]. The Annals of Statistics, 2007, 35:70-91.
[4] CAI T T, HALL P. Prediction in functional linear regression[J]. The Annals of Statistics, 2006, 34:2159-2179.
[5] ZHANG D W, LIN X H, SOWERS M. Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome[J]. Biometrics, 2007, 63(2):351-362.
[6] SHIN H. Partial functional linear regression[J]. Journal of Statistical Planning and Inference, 2009, 139:3405-3418.
[7] KOENKER R, BASSETT G. Regression quantiles[J]. Econometrica, 1978, 46:33-51.
[8] CARDOT H, CRAMBES C, SARDA P. Quantile regression when the covariates are functions[J]. Journal of Nonparametric Statistics, 2005, 17(7):841-856.
[9] KATO K. Estimation in functional linear quantile regression[J]. The Annals of Statistics, 2012, 40:3108-3136.
[10] 杜艳芳. 基于分位数回归的空气质量指数分析[D]. 兰州:兰州大学,2016. DU Yanfang. The analysis of air quality index based on quantile regression[D]. Lanzhou: Lanzhou University, 2016.
[11] 孙鸣茜. 函数型数据分位数回归模型及其应用[D]. 武汉:华中科技大学,2019. SUN Mingxi. Quantile regression of functional data and its application[D]. Wuhan: Huazhong University of Science and Technology, 2019.
[12] TANG Qingguo, CHENG Longsheng. Partial functional linear quantile regression[J]. Science China Mathematics, 2014, 57(12):2589-2608.
[13] KRAUS D. Components and completion of partially observed functional data[J]. Journal of the Royal Statistical Society, Series B: Statistical Methodology, 2015, 77(4):777-801.
[14] 王楚. 带有缺失数据的函数型响应部分函数线性回归模型的估计与应用[D]. 南京:南京理工大学,2021. WANG Chu. Estimation andapplication of partial functional linear regression model for function response with missing data[D]. Nanjing: Nanjing University of Science and Technology, 2021.
[15] KNEIP A, LIEBL D. On the optimal reconstruction of partially observed functional data[J]. The Annals of Statistics, 2020, 4:1692-1717.
[16] XIAO Juxia, XIE Tianfa, ZHANG Zhongzhan. Estimation in partially observed functional linear quantile regression[J]. Journal of Systems Science and Complexity, 2020, 35:313-341.
[17] CRAMBES C, DAAYEB C, GANNOUN A, et al. Functional linear model with partially observed covariate and missing values in the response[J]. Journal of Nonparametric Statistics, 2023, 35(1):172-197.
[18] BOSQ D. Linear processes in function spaces: theory and applications[M]. New York: Springer Science and Business Media, 2000.
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