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A robust nonparametric estimation of the autoregression function under an ergodic hypothesis
Author(s) -
La ïb Naämane,
OuldSa ÏD Elias
Publication year - 2000
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315918
Subject(s) - estimator , mathematics , autoregressive model , ergodic theory , nonparametric statistics , ergodicity , econometrics , consistency (knowledge bases) , nonparametric regression , strong consistency , kernel (algebra) , statistics , pure mathematics , discrete mathematics
The authors propose a family of robust nonparametric estimators for regression or autoregression functions based on kernel methods. They show the strong uniform consistency of these estimators under a general ergodicity condition when the data are unbounded and range over suitably increasing sequences of compact sets. They give some implications of these results for stating the prediction in Markovian processes with finite order and show, through simulation, the efficiency of the predictors they propose.