Functional Linear Regression
Dependence and Error Contamination
Bibliographic Data
| ID | 19417952 |
|---|---|
| Authors | Cheng Chen (0000-0002-3583-9370, London School of Economics and Political Science), Shaojun Guo (0000-0003-4262-4690, Renmin University of China, corresponding author), Xinghao Qiao (0000-0002-6546-6595, London School of Economics and Political Science) |
| Year | 2022 |
| Volume | 40 |
| Issue | 1 |
| Pages | 444-457 |
| Publication date | 2022-01-02 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Journal of Business and Economic Statistics (JOURNAL) |
| Journal identifiers | ISSN: 0735-0015 • E-ISSN: 1537-2707 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/07350015.2020.1832503 |
| OpenAlex | W3092316678 |
| Language | EN |
| Citations received | 3 |
| References cited | 24 |
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by iid measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this article, we consider functional linear regression with serially dependent observations of the functional predictor, when the contamination of the predictor by the white noise is genuinely functional with fully nonparametric covariance structure. Inspired by the fact that the autocovariance function of observed functional predictors automatically filters out the impact from the unobservable noise term, we propose a novel autocovariance-based generalized method-of-moments estimate of the slope function. We also develop a nonparametric smoothing approach to handle the scenario of partially observed functional predictors. The asymptotic properties of the resulting estimators under different scenarios are established. Finally, we demonstrate that our proposed method significantly outperforms possible competing methods through an extensive set of simulations and an analysis of a public financial dataset
Autocovariance · Covariance · Econometrics · Estimator · Functional data analysis · Functional principal component analysis · Nonparametric regression · Nonparametric statistics · Smoothing · Statistics · Advanced Statistical Methods and Models · Advanced Statistical Process Monitoring · Mathematics · Statistical Methods and Inference · Applied Mathematics
| Citations per year | 0.75 |
|---|---|
| Citation span | 2022 - 2026 (5) |
| Highly cited | No |