Using randomization to improve the performance of regression estimators under dependence
We consider a fixed-design regression model with long-range dependent errors which form a moving average process. Taking into account different behavior of regression estimators in such a model and in a randomdesign regression model discussed in Csörgő and Mielniczuk [5], we introduce an artificial...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2007
|
| Sorozat: | Acta scientiarum mathematicarum
73 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16216 |
| Tartalmi kivonat: | We consider a fixed-design regression model with long-range dependent errors which form a moving average process. Taking into account different behavior of regression estimators in such a model and in a randomdesign regression model discussed in Csörgő and Mielniczuk [5], we introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence of errors. The resulting estimator is shown to exhibit smoothing dichotomy with the variance in both cases tending to 0 more quickly than in the fixed design case. Moreover, we establish a uniform convergence rate of the regression function estimators which also reflects the dichotomous behaviour of the regression estimator. Simulation results indicate significant improvement for moderate sample sizes when randomization is employed. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 817-838 |
| ISSN: | 0001-6969 |