Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model
In the present paper, we study functional varying coefficient model in which both the response and the predictor are functions. We give estimates of the intercept and the slope functions in the case that the observations are sparse and noise-contaminated longitudinal data by using least squares repr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2017-08-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25883866.pdf |
| _version_ | 1817981092384210944 |
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| author | Behdad Mostafaiy Mohammad Reza Faridrohani |
| author_facet | Behdad Mostafaiy Mohammad Reza Faridrohani |
| author_sort | Behdad Mostafaiy |
| collection | DOAJ |
| description | In the present paper, we study functional varying coefficient model in which both the response and the predictor are functions. We give estimates of the intercept and the slope functions in the case that the observations are sparse and noise-contaminated longitudinal data by using least squares representation of the model parameters. To estimate the parameter functions involved in the representation, we use a regularization method in some reproducing kernel Hilbert spaces. As we will see, our procedure is easy to implement. Also, we obtain the convergence rates of the estimators in the <i>L</i><sup>2</sup>-sense. These convergence rates establish that the procedure performs well, especially, when sampling frequency or sample size increases. |
| first_indexed | 2024-04-13T23:02:27Z |
| format | Article |
| id | doaj.art-faf83ba8396f45eab7f4954d01da4e1f |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-13T23:02:27Z |
| publishDate | 2017-08-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-faf83ba8396f45eab7f4954d01da4e1f2022-12-22T02:25:49ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872017-08-0116310.2991/jsta.2017.16.3.5Least Squares Parameter Estimation for Sparse Functional Varying Coefficient ModelBehdad MostafaiyMohammad Reza FaridrohaniIn the present paper, we study functional varying coefficient model in which both the response and the predictor are functions. We give estimates of the intercept and the slope functions in the case that the observations are sparse and noise-contaminated longitudinal data by using least squares representation of the model parameters. To estimate the parameter functions involved in the representation, we use a regularization method in some reproducing kernel Hilbert spaces. As we will see, our procedure is easy to implement. Also, we obtain the convergence rates of the estimators in the <i>L</i><sup>2</sup>-sense. These convergence rates establish that the procedure performs well, especially, when sampling frequency or sample size increases.https://www.atlantis-press.com/article/25883866.pdfFunctional varying coefficient model; Longitudinal data Analysis; Rate of convergence; Regularization; Reproducing kernel Hilbert space; Sparsity. |
| spellingShingle | Behdad Mostafaiy Mohammad Reza Faridrohani Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model Journal of Statistical Theory and Applications (JSTA) Functional varying coefficient model; Longitudinal data Analysis; Rate of convergence; Regularization; Reproducing kernel Hilbert space; Sparsity. |
| title | Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model |
| title_full | Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model |
| title_fullStr | Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model |
| title_full_unstemmed | Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model |
| title_short | Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model |
| title_sort | least squares parameter estimation for sparse functional varying coefficient model |
| topic | Functional varying coefficient model; Longitudinal data Analysis; Rate of convergence; Regularization; Reproducing kernel Hilbert space; Sparsity. |
| url | https://www.atlantis-press.com/article/25883866.pdf |
| work_keys_str_mv | AT behdadmostafaiy leastsquaresparameterestimationforsparsefunctionalvaryingcoefficientmodel AT mohammadrezafaridrohani leastsquaresparameterestimationforsparsefunctionalvaryingcoefficientmodel |