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Asymptotic behaviour of M‐estimators in AR(p) models under nonstandard conditions
Author(s) -
El Bantli Faouzi,
Hallin Marc
Publication year - 2001
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 - 10.2307/3316058
Subject(s) - estimator , quantile , mathematics , asymptotic distribution , autoregressive model , context (archaeology) , classification of discontinuities , gaussian , limiting , statistics , econometrics , mathematical analysis , physics , mechanical engineering , paleontology , quantum mechanics , engineering , biology
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 L 1 ‐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.