Uniform consistency rate of kNN regression estimation for functional time series data

被引:18
作者
Ling, Nengxiang [1 ]
Meng, Shuyu [1 ,2 ]
Vieu, Philippe [3 ]
机构
[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China
[2] Nanjing Univ Sci & Technol, Sch Sci, Nanjing, Jiangsu, Peoples R China
[3] Univ Paul Sabatier, Inst Math, Toulouse, France
关键词
kNN estimation; nonparametric functional data analysis; strong mixing dependence; uniform almost complete convergence rate; NONPARAMETRIC REGRESSION; ASYMPTOTIC NORMALITY;
D O I
10.1080/10485252.2019.1583338
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.
引用
收藏
页码:451 / 468
页数:18
相关论文
共 39 条
  • [1] Aneiros G., 2019, J NONPARAMETRIC STAT
  • [2] Aneiros G., 2019, J MULTIVARIATE ANAL, V170
  • [3] An introduction to the 4th edition of the InternationalWorkshop on Functional and Operatorial Statistics
    Aneiros, German
    Bongiorno, Enea G.
    Cao, Ricardo
    Vieu, Philippe
    [J]. FUNCTIONAL STATISTICS AND RELATED FIELDS, 2017, : 1 - 5
  • [4] Attouch MK, 2012, MAT VESTN, V64, P275
  • [5] Local linear regression for functional predictor and scalar response
    Baillo, Amparo
    Grane, Aurea
    [J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2009, 100 (01) : 102 - 111
  • [6] Locally modelled regression and functional data
    Barrientos-Marin, J.
    Ferraty, F.
    Vieu, P.
    [J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2010, 22 (05) : 617 - 632
  • [7] Rates of Convergence of the Functional k-Nearest Neighbor Estimate
    Biau, Gerard
    Cerou, Frederic
    Guyader, Arnaud
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (04) : 2034 - 2040
  • [8] GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY
    BOLLERSLEV, T
    [J]. JOURNAL OF ECONOMETRICS, 1986, 31 (03) : 307 - 327
  • [9] Bosq D., 2000, Linear Processes in Function Space: Theory and Applications
  • [10] k-Nearest Neighbour method in functional nonparametric regression
    Burba, Florent
    Ferraty, Frederic
    Vieu, Philippe
    [J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2009, 21 (04) : 453 - 469