Asymptotic behavior of M-estimators in AR(p) models under nonstandard conditions

Marc Hallin and Faouzi El Bantli

ULB Institutional Repository from ULB -- Universite Libre de Bruxelles

Abstract: The authors derive the limiting distribution of M-estimators in AR(p) models under nonstandard conditions, allowing for discontinuities in score and density functions. Unlike usual regularity assumptions, these conditions are satisfied in the context of L1-estimation and autoregression quantiles. The asymptotic distributions of the resulting estimators, however, are not generally Gaussian. Moreover, their bootstrap approximations are consistent along very specific sequences of bootstrap sample sizes only.

Date: 2001-03
Note: FLWIN
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Published in: Canadian Journal of Statistics (2001) v.29 n° 1,p.155-168

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