Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model
This paper deals with the conditional density estimator of a real response variable given a functional random variable (i.e., takes values in an infinite-dimensional space). Specifically, we focus on the functional index model, and this approach represents a good compromise between nonparametric and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2022-08-01
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| Series: | Statistical Theory and Related Fields |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/24754269.2021.1965945 |
| _version_ | 1827809285409603584 |
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| author | Fadila Benaissa Abdelmalek Gagui Abdelhak Chouaf |
| author_facet | Fadila Benaissa Abdelmalek Gagui Abdelhak Chouaf |
| author_sort | Fadila Benaissa |
| collection | DOAJ |
| description | This paper deals with the conditional density estimator of a real response variable given a functional random variable (i.e., takes values in an infinite-dimensional space). Specifically, we focus on the functional index model, and this approach represents a good compromise between nonparametric and parametric models. Then we give under general conditions and when the variables are independent, the quadratic error and asymptotic normality of estimator by local linear method, based on the single-index structure. Finally, we complete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area. |
| first_indexed | 2024-03-11T22:38:59Z |
| format | Article |
| id | doaj.art-a8ff188e9e624f998a6637531816e23d |
| institution | Directory Open Access Journal |
| issn | 2475-4269 2475-4277 |
| language | English |
| last_indexed | 2024-03-11T22:38:59Z |
| publishDate | 2022-08-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Statistical Theory and Related Fields |
| spelling | doaj.art-a8ff188e9e624f998a6637531816e23d2023-09-22T09:19:46ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772022-08-016320821910.1080/24754269.2021.19659451965945Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index modelFadila Benaissa0Abdelmalek Gagui1Abdelhak Chouaf2University Oran 1 Ahmed Ben Bella OranDjillali Liabes UniversityDjillali Liabes UniversityThis paper deals with the conditional density estimator of a real response variable given a functional random variable (i.e., takes values in an infinite-dimensional space). Specifically, we focus on the functional index model, and this approach represents a good compromise between nonparametric and parametric models. Then we give under general conditions and when the variables are independent, the quadratic error and asymptotic normality of estimator by local linear method, based on the single-index structure. Finally, we complete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.http://dx.doi.org/10.1080/24754269.2021.1965945mean squared errorsingle functional indexconditional density functionnonparametric estimationlocal linear estimationasymptotic normalityfunctional data |
| spellingShingle | Fadila Benaissa Abdelmalek Gagui Abdelhak Chouaf Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model Statistical Theory and Related Fields mean squared error single functional index conditional density function nonparametric estimation local linear estimation asymptotic normality functional data |
| title | Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model |
| title_full | Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model |
| title_fullStr | Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model |
| title_full_unstemmed | Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model |
| title_short | Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model |
| title_sort | asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single index model |
| topic | mean squared error single functional index conditional density function nonparametric estimation local linear estimation asymptotic normality functional data |
| url | http://dx.doi.org/10.1080/24754269.2021.1965945 |
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