Abstract
A local linear kernel estimator of the regression function x → g(x) := E[Y i|X i = x], x ε ℝ d, of a stationary (d + 1)-dimensional spatial process {(Y i, X i), i ε ℤ N} observed over a rectangular domain of the form l n := {i = (i 1,...,i N) ε ℤ N |1 ≤ i k ≤ n k, k = 1,..., N}, n = (n 1,..., n N) ε ℤ N is proposed and investigated. Under mild regularity assumptions, asymptotic normality of the estimators of g(x) and its derivatives is established. Appropriate choices of the bandwidths are proposed. The spatial process is assumed to satisfy some very general mixing conditions, generalizing classical time-series strong mixing concepts. The size of the rectangular domain l n is allowed to tend to infinity at different rates depending on the direction in ℤ N. © Institute of Mathematical Statistics, 2004.
| Original language | English |
|---|---|
| Pages (from-to) | 2469-2500 |
| Journal | Annals of Statistics |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Dec 2004 |
| 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
- Asymptotic normality
- Local linear kernel estimate
- Mixing random field
- Spatial regression