Framelet block thresholding estimator for sparse functional data

Chen，Di Rong1; Cheng，Kun1; Liu，Chao2

2021

10.1016/j.jmva.2021.104895

JOURNAL OF MULTIVARIATE ANALYSIS   影响因子和分区

0047-259X

1095-7243

Nonparametric estimation of mean and covariance functions based on discretely observed data is important in functional data analysis. In this paper, we propose a framelet block thresholding method for the case of sparsely observed functional data. The procedure is easily implemented and the resultant estimators are represented as explicit B-spline expressions. For sparsely observed functional data, we establish, under some mild conditions but without knowing the smoothness parameter, convergence rates of mean integrated squared errors for mean and covariance estimators respectively. In particular, the mean estimator attains minimax optimal rate. The simulated and real data examples are provided to offer empirical support of the theoretical properties. Compared to the existing methods, the proposed method outperforms in adapting automatically to local variations.

Block thresholding Sparse functional data Tight framelets

英语

其他

MATHEMATICS

2-s2.0-85118987489

Scopus

1.School of Mathematical Sciences,Beihang University,Beijing,100191,China
2.Department of Statistics and Data Science,The Southern University of Science and Technology,Shenzhen,518055,China

Chen，Di Rong,Cheng，Kun,Liu，Chao. Framelet block thresholding estimator for sparse functional data[J]. JOURNAL OF MULTIVARIATE ANALYSIS,2021,189.

Chen，Di Rong,Cheng，Kun,&Liu，Chao.(2021).Framelet block thresholding estimator for sparse functional data.JOURNAL OF MULTIVARIATE ANALYSIS,189.

Chen，Di Rong,et al."Framelet block thresholding estimator for sparse functional data".JOURNAL OF MULTIVARIATE ANALYSIS 189(2021).