Abstract
The local qualitative robustness of GM-tests against outliers in the autoregression model is studied in the paper. A local scheme of data contamination by independent outliers with the intensity O(n −1/2) is considered. The qualitative robustness in terms of power equicontinuity is obtained. The GM-tests asymptotically optimal in the maximin sense are constructed.
This is a preview of subscription content, log in via an institution to check access.
References
F. R. Hampel, E. M. Ronchetti, J. Rousseeuw, and W. A. Stahel, Robust Statistics. The Approach Based on Influence Functions (Wiley, N.Y., 1985).
H. L. Koul, Weighted Empiricals and Linear Models. IMS Lect. Notes. Monogr. Series, Vol. 21 (Hayward, CA, 1992).
D. M. Esaulov, “Robustness of GM-Tests in Autoregression Against Outliers,” Vestn. Mosk. Univ., Matem. Mekhan. No. 2, 47 (2012).
R. D. Martin and V. J. Yoliai, “Influence Functionals for Time Series,” Ann. Statist. 14, 781 (1986).
M. V. Boldin, “On Empirical Processes in Heteroscedastic Time Series and Their Use for Hypothesis Testing and Estimation,” Math. Methods Statist. 9, 65 (2000).
M. V. Boldin, “Local Robustness of Sign Tests in AR(1) Against Outliers,” Math. Methods Statist. 20, 1 (2011).
H. Reider, “Qualitative Robustness of Rank Tests,” Ann. Statist. 10, 205 (1982).
M. V. Boldin, “On Median Estimates and Tests in Autoregressive Models,” Math. Methods Statist. 3, 114 (1994).
Author information
Authors and Affiliations
Additional information
Original Russian Text © M. V. Boldin, D.M. Esaulov, 2014, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2014, Vol. 69, No. 1, pp. 46–50.
About this article
Cite this article
Boldin, M.V., Esaulov, D.M. Residual empirical processes and qualitatively robust GM-tests in autoregression. Moscow Univ. Math. Bull. 69, 29–32 (2014). https://doi.org/10.3103/S0027132214010057
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027132214010057