Abstract
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-δ-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 β-mixing processes.
| Original language | English |
|---|---|
| Pages (from-to) | 177-197 |
| Journal | Statistica Sinica |
| Volume | 17 |
| Issue number | 1 |
| Publication status | Published - Jan 2007 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- β-mixing
- Adaptive varying-coefficient model
- Asymptotic normality
- Empirical process
- Index parameter
- Root-n consistency
- Uniform convergence
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