The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data. (English) Zbl 1461.62239
Summary: The aim of this paper is to nonparametrically estimate the expectile regression in the case of a functional predictor and a scalar response. More precisely, we construct a kernel-type estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the expectile regression estimator. Precisely, we establish the almost complete convergence with rate. Furthermore, we obtain the asymptotic normality of the proposed estimator under some mild conditions. We provide how to apply our results to construct the confidence intervals. The case of functional predictor is of particular interest and challenge, both from theoretical as well as practical point of view. We discuss the potential impacts of functional expectile regression in NFDA with a particular focus on the supervised classification, prediction and financial risk analysis problems. Finally, the finite-sample performances of the model and the estimation method are illustrated using the analysis of simulated data and real data coming from the financial risk analysis.
MSC:
| 62R10 | Functional data analysis |
| 62E20 | Asymptotic distribution theory in statistics |
| 62G08 | Nonparametric regression and quantile regression |
| 62G10 | Nonparametric hypothesis testing |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
nonparametric estimation; kernel type function estimator; risk measure; asymmetric least squares regression; expectiles; functional data; almost consistency; asymptotic normality; probability convergence; strong mixing processSoftware:
fda (R)References:
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