ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY
We establish the asymptotic theory for the estimation of adaptive varying coefficient linear models. More specifically, we show that the estimator of the index parameter is root-n-consistent. It differs from the locally optimal estimator that has been proposed in the literature with a prerequisite t...
| Main Authors: | , , |
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| Format: | Journal Article |
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International Chinese Statistical Association
2007
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| Online Access: | http://www3.stat.sinica.edu.tw/statistica/ http://hdl.handle.net/20.500.11937/15799 |
| _version_ | 1848748991630540800 |
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| author | Lu, Zudi Tjostheim, D. YAO, Q. |
| author_facet | Lu, Zudi Tjostheim, D. YAO, Q. |
| author_sort | Lu, Zudi |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We establish the asymptotic theory for the estimation of adaptive varying coefficient linear models. More specifically, we show that the estimator of the index parameter is root-n-consistent. It differs from the locally optimal estimator that has been proposed in the literature with a prerequisite that the estimator is within a n^{-delta} distance of the true value. To this end, we establish two fundamental lemmas for the asymptotic properties of the estimators of parametric components in a general semiparametric setting. Furthermore, the estimation for the coefficient functions is asymptotically adaptive to the unknown index parameter. Asymptotic properties are derived using the empirical process theory for strictly stationary beta-mixing processes. |
| first_indexed | 2025-11-14T07:13:50Z |
| format | Journal Article |
| id | curtin-20.500.11937-15799 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:13:50Z |
| publishDate | 2007 |
| publisher | International Chinese Statistical Association |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-157992017-02-28T01:27:07Z ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY Lu, Zudi Tjostheim, D. YAO, Q. uniform convergence empirical process root-n consistency - beta-mixing Adaptive varying-coefficient model asymptotic normality index parameter We establish the asymptotic theory for the estimation of adaptive varying coefficient linear models. More specifically, we show that the estimator of the index parameter is root-n-consistent. It differs from the locally optimal estimator that has been proposed in the literature with a prerequisite that the estimator is within a n^{-delta} distance of the true value. To this end, we establish two fundamental lemmas for the asymptotic properties of the estimators of parametric components in a general semiparametric setting. Furthermore, the estimation for the coefficient functions is asymptotically adaptive to the unknown index parameter. Asymptotic properties are derived using the empirical process theory for strictly stationary beta-mixing processes. 2007 Journal Article http://hdl.handle.net/20.500.11937/15799 http://www3.stat.sinica.edu.tw/statistica/ International Chinese Statistical Association restricted |
| spellingShingle | uniform convergence empirical process root-n consistency - beta-mixing Adaptive varying-coefficient model asymptotic normality index parameter Lu, Zudi Tjostheim, D. YAO, Q. ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title | ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title_full | ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title_fullStr | ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title_full_unstemmed | ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title_short | ADAPTIVE VARYING-COEFFICIENT LINEAR MODELS FOR STOCHASTIC PROCESSES: ASYMPTOTIC THEORY |
| title_sort | adaptive varying-coefficient linear models for stochastic processes: asymptotic theory |
| topic | uniform convergence empirical process root-n consistency - beta-mixing Adaptive varying-coefficient model asymptotic normality index parameter |
| url | http://www3.stat.sinica.edu.tw/statistica/ http://hdl.handle.net/20.500.11937/15799 |