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

Canadian Journal of Statistics

Volumn 29, Issue 1, 2001, Pages 155-168

  El Bantli, Faouzi ^a   Hallin, Marc ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Autoregression quantiles; Autoregressive model; Bootstrap; Limiting distribution; M estimators

Indexed keywords

EID: 0035636487     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316058     Document Type: Article

References (27)

1. p regression estimators. Econometric Theory, 12, 257-283.
2. Z. D. Bai & Y. Wu (1997). General M-estimation. Journal of Multivariate Analysis, 63, 119-135.
3. P. Bickel & D. A. Freedman (1981). Some asymptotic theory for the bootstrap. The Annals of Statistics, 9, 1196-1217.
4. H. O. Bustos (1982). General M-estimates for contaminated pth-order autoregressive processes: consistency and asymptotic normality. Zeitschrift für Wahrscheinlichkeitsheorie und verwandte Gebiete, 59, 491-504.
5. C. J. Geyer (1996). On the asymptotics of convex stochastic optimization. Unpublished manuscript, University of Minnesota.
6. P. Hall & C. C. Heyde (1980). Martingale Limit Theory and its Applications. Academic Press, New York.
7. M. Hallin & B. J. M. Werker (1999). Optimal testing for semi-parametric AR models: from Gaussian Lagrange multipliers to autoregression rank scores and adaptive rank tests. In Asymptotics, Nonparametrics and Time Series (S. Ghosh, ed.), Marcel Dekker, New York, pp. 295-350.
8. G. Heimann & J. P. Kreiss (1996). Bootstrapping general first order autoregression. Statistics and Probability Letters, 30, 87-98.
9. N. L. Hjørt & D. Pollard (1993). Asymptotics for minimizers of convex processes. Statistical Research Report, University of Oslo, Oslo, Norway.
10. J. S. Huang, P. K. Sen & J. Shao (1996). Bootstrapping a sample quantile when the density has a jump. Statistica Sinica, 6, 299-309.
11. P. J. Huber (1973). Robust regression: asymptotics, conjectures, and Monte-Carlo. The Annals of Statistics, 1, 799-821.
12. I. A. Ibragimov & R. Z. Has'minskii (1981). Statistical Estimation: Asymptotic Theory. Springer-Verlag, New York.
13. J. Jurečková (1983). Asymptotic behavior of M-estimators of location in nonregular cases. Statistics and Decisions, 1, 323-340.
14. J. Jurečková & P. K. Sen (1996). Robust Statistical Procedures: Asymptotics and Interrelations. Wiley, New York.
15. 1-norm and Related Methods, Neuchâtel (Switzerland), August 11-15, 1997 (Y. Dodge, ed.), IMS Lecture Notes-Monograph Series, vol. 31, pp. 315-328.
16. K. Knight (1998). Bootstrapping samples quantiles in non-regular cases. Statistics and Probability Letters, 37, 259-267.
17. H. L. Koul (1991). A weak convergence result useful in robust autoregression. Journal of Statistical Planning and Inference, 29, 291-308.
18. H. L. Koul & A. K. Md. E. Saleh (1995). Autoregression quantiles and related rank score processes. The Annals of Statistics, 23, 670-689.
19. J. P. Kreiss (1985). A note on M-estimation in stationary ARMA processes. Statistics and Decisions, 3, 317-336.
20. J. P. Kreiss & J. Franke (1992). Bootstrapping stationary autoregressive-moving average models. Journal of Time Series Analysis, 13, 297-317.
21. J. Kuelbs & R. Lepage (1973). The law of the iterated logarithm for Brownian motion in a Banach space. Transactions of the American Mathematical Society, 185, 235-265.
22. R. D. Martin (1980). Robust estimation of autoregressive models. With comments by Robert B. Miller. In Directions in Time Series: Proceedings of the IMS Special Topics Meeting on Time Series Analysis, Iowa State University, Ames (Iowa), May 1-3, 1978 (D. R. Brillinger & G. C. Tiao, eds.), pp. 228-262.
23. R. D. Martin & V. J. Yohai (1985). Robustness in time series and estimating ARMA models. In Handbook of Statistics 5 (E. J. Hannan, P. K. Krishnaiah & M. M. Rao, eds.), North-Holland, Amsterdam, pp. 119-155.
24. D. Monrad & W. Philipp (1991). Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales. Probability Theory and Related Fields, 88, 381-404.
25. D. Pollard (1984). Convergence of Stochastic Processes. Springer-Verlag, New York.
26. D. Pollard (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory, 7, 186-199.
27. p-estimates. In Robust Regression, Analysis and Applications (K. D. Lawrence & J. L. Arthur, eds.), Marcel Dekker, New York, pp. 23-85.