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High-Dimensional Statistics: Non-Parametric Generalized Functional Partially Linear Single-Index Model
| Content Provider | MDPI |
|---|---|
| Author | Alahiane, Mohamed Ouassou, Idir Rachdi, Mustapha Vieu, Philippe |
| Copyright Year | 2022 |
| Description | We study the non-parametric estimation of partially linear generalized single-index functional models, where the systematic component of the model has a flexible functional semi-parametric form with a general link function. We suggest an efficient and practical approach to estimate (I) the single-index link function, (II) the single-index coefficients as well as (III) the non-parametric functional component of the model. The estimation procedure is developed by applying quasi-likelihood, polynomial splines and kernel smoothings. We then derive the asymptotic properties, with rates, of the estimators of each component of the model. Their asymptotic normality is also established. By making use of the splines approximation and the Fisher scoring algorithm, we show that our approach has numerical advantages in terms of the practical efficiency and the computational stability. A computational study on data is provided to illustrate the good practical behavior of our methodology. |
| Starting Page | 2704 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math10152704 |
| Journal | Mathematics |
| Issue Number | 15 |
| Volume Number | 10 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2022-07-30 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Mathematical Social Sciences Statistics and Probability Functional Data Analysis Generalized Linear Model Polynomial Splines Quasi-likelihood Semi-parametric Regression the Kernel Estimator of the Regression Operator Single-index Model Fisher Scoring Algorithm Asymptotic Normality |
| Content Type | Text |
| Resource Type | Article |
