Single index regression for locally stationary functional time series
In this research, we formulated an asymptotic theory for single index regression applied to locally stationary functional time series. Our approach involved introducing estimators featuring a regression function that exhibited smooth temporal changes. We rigorously established the uniform convergenc...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241719 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590743393271808 |
|---|---|
| author | Breix Michael Agua Salim Bouzebda |
| author_facet | Breix Michael Agua Salim Bouzebda |
| author_sort | Breix Michael Agua |
| collection | DOAJ |
| description | In this research, we formulated an asymptotic theory for single index regression applied to locally stationary functional time series. Our approach involved introducing estimators featuring a regression function that exhibited smooth temporal changes. We rigorously established the uniform convergence rates for kernel estimators, specifically the Nadaraya-Watson (NW) estimator for the regression function. Additionally, we provided a central limit theorem for the NW estimator. Finally, the theory was supported by a comprehensive simulation study to investigate the finite-sample performance of our proposed method. |
| format | Article |
| id | doaj-art-55663959a8fd45ff81bd80f20870038c |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-55663959a8fd45ff81bd80f20870038c2025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912362023625810.3934/math.20241719Single index regression for locally stationary functional time seriesBreix Michael Agua0Salim Bouzebda1Université de technologie de Compiègne, Laboratory of Applied Mathematics of Compiègne (LMAC), CS 60319 - 57 avenue de Landshut, Compiègne, FranceUniversité de technologie de Compiègne, Laboratory of Applied Mathematics of Compiègne (LMAC), CS 60319 - 57 avenue de Landshut, Compiègne, FranceIn this research, we formulated an asymptotic theory for single index regression applied to locally stationary functional time series. Our approach involved introducing estimators featuring a regression function that exhibited smooth temporal changes. We rigorously established the uniform convergence rates for kernel estimators, specifically the Nadaraya-Watson (NW) estimator for the regression function. Additionally, we provided a central limit theorem for the NW estimator. Finally, the theory was supported by a comprehensive simulation study to investigate the finite-sample performance of our proposed method.https://www.aimspress.com/article/doi/10.3934/math.20241719convergence ratesexponential inequalitykernel regressionfunctional time serieslocally stationary processsingle index modelfunctional data analysis |
| spellingShingle | Breix Michael Agua Salim Bouzebda Single index regression for locally stationary functional time series AIMS Mathematics convergence rates exponential inequality kernel regression functional time series locally stationary process single index model functional data analysis |
| title | Single index regression for locally stationary functional time series |
| title_full | Single index regression for locally stationary functional time series |
| title_fullStr | Single index regression for locally stationary functional time series |
| title_full_unstemmed | Single index regression for locally stationary functional time series |
| title_short | Single index regression for locally stationary functional time series |
| title_sort | single index regression for locally stationary functional time series |
| topic | convergence rates exponential inequality kernel regression functional time series locally stationary process single index model functional data analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241719 |
| work_keys_str_mv | AT breixmichaelagua singleindexregressionforlocallystationaryfunctionaltimeseries AT salimbouzebda singleindexregressionforlocallystationaryfunctionaltimeseries |