M-estimation of linear models with dependent errors

Details M-estimation of linear models with dependent errors M-estimation of linear models with dependent errors

2004-12-14

arxiv.org/abs/math/0412268v3

Annals of Statistics 2007, Vol. 35, No. 2, 495-521

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001406 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001406

We study asymptotic properties of $M$-estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the $M$-estimates are derived and a central limit theorem is established. The results are applied to linear models with errors being short-range dependent linear processes, heavy-tailed linear processes and some widely used nonlinear time series.

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