Geodesic
Robustness of sign tests for testing hypotheses about order of autoregression
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 761-768 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Observations of autoregression are contaminated by additive isolated outliers with an unknown random distribution. Intensity of the outliers $\gamma_n$ is $\min(1,n^{-1/2}\gamma)$, where $\gamma \geqq 0$ is unknown, and $n$ is the data size. Robustness of sign tests for hypotheses about order of autoregression is considered. The result is formulated in terms of equicontinuity of limiting power with respect to $\gamma$ at $\gamma=0$.
Keywords: robustness against outliers; equicontinuity of power. 
@article{TVP_2012_57_4_a7,
     author = {M. V. Boldin},
     title = {Robustness of sign tests for testing hypotheses about order of autoregression},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {761--768},
     year = {2012},
     volume = {57},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a7/}
}
TY  - JOUR
AU  - M. V. Boldin
TI  - Robustness of sign tests for testing hypotheses about order of autoregression
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2012
SP  - 761
EP  - 768
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a7/
LA  - ru
ID  - TVP_2012_57_4_a7
ER  - 
%0 Journal Article
%A M. V. Boldin
%T Robustness of sign tests for testing hypotheses about order of autoregression
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2012
%P 761-768
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a7/
%G ru
%F TVP_2012_57_4_a7
M. V. Boldin. Robustness of sign tests for testing hypotheses about order of autoregression. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 761-768. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a7/

[1] Boldin M. V., Shtute V., “O znakovykh testakh v $ARMA$ modeli s vozmozhno beskonechnoi dispersiei oshibok”, Teoriya veroyatn. i ee primen., 49:3 (2004), 436–460 | MR

[2] Esaulov D., “Robastnost GM-testov v avtoregressii protiv vybrosov”, Vestn. MGU, ser. Matem. mekh., 2011, no. 5, 5–9

[3] Anderson T., Statisticheskii analiz vremennýkh ryadov, Mir, M., 1976, 755 pp.

[4] Boldin M. V., Tyurin Yu. N., “On nonparametric sign procedures for autoregression models”, Math. Methods Statist., 3:4 (1994), 279–305 | MR | Zbl

[5] Boldin M. V., Simonova G. I., Tyurin Yu. N., Sign-based methods in linear statistical models, Amer. Math. Soc., Providence, 1997, 234 pp. | MR | Zbl

[6] Boldin M. V., “Local robustness of sign tests in $AR(1)$ against outliers”, Math. Methods Statist., 20:1 (2011), 1–13 | DOI | MR

[7] Hampel F. R., Ronchetti E. M., Rousseeuw P. J., Stahel W. A., Robust Statistics. The Approach Based on Influence Functions, Wiley, New York, 1986, 502 pp. | MR | Zbl

[8] Hallin M., Puri M. L., “Optimal rank-based procedures for time series analysis: testing an ARMA model against other ARMA models”, Ann. Statist., 16:1 (1988), 402–432 | DOI | MR | Zbl

[9] Hallin M., Puri M. L., “Time series analysis via rank order theory: signed-rank tests for ARMA models”, J. Multivariate Anal., 39:1 (1991), 1–29 | DOI | MR | Zbl

[10] Hallin M., Puri M. L., “Aligned rank test for linear models with autocorrelated error terms”, J. Multivariate Anal., 50:2 (1994), 175–237 | DOI | MR | Zbl

[11] Kreiss J.-P., “Testing linear hypotheses in autoregression”, Ann. Statist., 18:3 (1990), 1470–1482 | DOI | MR | Zbl

[12] Martin R. D., Yohai V. J., “Influence functionals for time series”, Ann. Statist., 14:3 (1986), 781–818 | DOI | MR | Zbl