Abstract
Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required. © Springer-Verlag 2002.
| Original language | English |
|---|---|
| Pages (from-to) | 641-656 |
| Journal | Acta Mathematicae Applicatae Sinica |
| Volume | 18 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2002 |
| 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
- Bandwidth
- Kernel estimator
- Mixing
- Non-isotropic
- Spatial conditional regression
- Spatial data
- Weak consistency and rates