Abstract
Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the so-called optimal bandwidth h(n) = O(vertical bar n vertical bar(-1/5)), n epsilon Z(d), is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(vertical bar n vertical bar(-4/5) log vertical bar n vertical bar). Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.
Original language | English |
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Pages (from-to) | 1871-1882 |
Number of pages | 12 |
Journal | Acta mathematica sinica-English series |
Volume | 24 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Nov 2008 |
Keywords
- strongly mixing
- Bahadur representation
- RANDOM-FIELDS
- LOCAL M-ESTIMATOR
- TIME-SERIES
- MODELS
- local linear M-estimator
- REGRESSION
- spatial processes
- DENSITY-ESTIMATION