zbMATH — the first resource for mathematics

Modelling functional data with high-dimensional error structure. (English) Zbl 1444.62153
Aneiros, Germán (ed.) et al., Functional and high-dimensional statistics and related fields. Selected papers presented at the 5th international workshop on functional and operatorial statistics, IWFOS 2021, Brno, Czech Republic, June 23–25, 2021. Cham: Springer. Contrib. Stat., 99-106 (2020).
Summary: We propose to model raw functional data as a mixture of functions and high-dimensional error. The conventional approach to retrieve the functional component from raw data is through varied smoothing techniques. Nevertheless, smoothing itself may not be adequate when measurement error exists. We propose to use factor model to reduce the dimension of the high-dimensional measurement error, while smoothing the functional component. Our model also provides as an alternative for modelling functional data with step jump. Regularized least squares method is used to find the model estimates. We look at the asymptotic behaviour of the estimator when both the sample size and the number of points per curve go to infinity and the limiting distribution is derived.
For the entire collection see [Zbl 1446.62001].
62R10 Functional data analysis
62E20 Asymptotic distribution theory in statistics
fda (R); KernSmooth
Full Text: DOI
[1] Bai, J.: Inferential theory for factor models of large dimensions. Econometrica 71(1), 135-171 (2003) · Zbl 1136.62354
[2] Cai, T.T., Yuan, M.: Optimal estimation of the mean function based on discretely sampled functional data: Phase transition. The annals of statistics39(5), 2330-2355 (2011) · Zbl 1231.62040
[3] Cuevas, A.: A partial overview of the theory of statistics with functional data. Journal of Statistical Planning and Inference147, 1-23 (2014) · Zbl 1278.62012
[4] Eubank, R.L.: Nonparametric Regression and Spline Smoothing. CRC press (1999) · Zbl 0936.62044
[5] Fan, J., Fan, Y., Lv, J.: High dimensional covariance matrix estimation using a factor model. Journal of Econometrics147(1), 186-197 (2008) · Zbl 1429.62185
[6] Fan, J., Gijbels, I.: Local Polynomial Modelling and Its Applications. Chapman & Hall, London (1996) · Zbl 0873.62037
[7] Febrero-Bande, M., Galeano, P., González-Manteiga, W.: Functional principal component regression and functional partial least-squares regression: An overview and a comparative study. International Statistical Review85(1), 61- 83 (2017)
[8] Goia, A., Vieu, P.: An introduction to recent advances in high/infinite dimensional statistics. Journal of Multivariate Analysis146, 1-6 (2016) · Zbl 1384.00073
[9] Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman & Hall, London (1999) · Zbl 0832.62032
[10] Lam, C., Yao, Q., Bathia, N.: Estimation of latent factors for high-dimensional time series. Biometrika98(4), 901-918 (2011) · Zbl 1228.62110
[11] Ramsay, J.O., Hooker, G.: Dynamic Data Analysis: Modeling Data with Differential Equations. Springer, New York (2017) · Zbl 1382.62001
[12] Ramsay, J.O., Silverman, B.W.: Applied Functional Data Analysis. Springer, New York (2002) · Zbl 1011.62002
[13] Ramsay, J.O., Silverman, B.W.: Functional Data Analysis. Springer, New York (2005) · Zbl 1079.62006
[14] Reiss, P.T., Goldsmith, J., Shang, H.L., Ogden, R.T.: Methods for scalar-onfunction regression. International Statistical Review85(2), 228-249 (2017)
[15] Wahba, G.: Spline models for observational data, vol. 59. Siam (1990) · Zbl 0813.62001
[16] Wand, M.P., Jones, C.M.: Kernel Smoothing. Chapman & Hall (1995) · Zbl 0854.62043
[17] Wang, J.L., Chiou, J.M., Müller, H.G.: Functional data analysis. Annual Review of Statistics and Its Application3, 257-295 (2016)
[18] Yao, W., Li, R.: New local estimation procedure for a non-parametric regression function for longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology)75(1), 123-138 (2013)
[19] Zhang, X.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.