Geodesic
Rate of convergence for a class of RCA estimators
Kybernetika, Tome 42 (2006) no. 6, pp. 699-709 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
Classification : 60F05, 60G10, 62F10, 62M09, 62M10, 91B84
Keywords: RCA; parameter estimation; rate of convergence 
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     title = {Rate of convergence for a class of {RCA} estimators},
     journal = {Kybernetika},
     pages = {699--709},
     year = {2006},
     volume = {42},
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     zbl = {1249.60034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006_42_6_a4/}
}
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Vaněček, Pavel. Rate of convergence for a class of RCA estimators. Kybernetika, Tome 42 (2006) no. 6, pp. 699-709. http://geodesic.mathdoc.fr/item/KYB_2006_42_6_a4/

[1] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in general autoregressive model. Statistics 21 (1990), 461–470 | DOI | MR

[2] Basu A. K., Roy S. Sen: On rates of convergence in the central limit theorem for parameter estimation in random coefficient autoregressive models. J. Indian Statist. Assoc. 26 (1988), 19–25 | MR

[3] Davidson J.: Stochastic Limit Theory. (Advanced Texts in Econometrics.) Oxford University Press, New York, Reprinted 2002 | MR | Zbl

[5] Janečková H., Prášková Z.: CWLS and ML estimates in a heteroscedastic RCA(1) model. Statist. Decisions 22 (2004), 245–259 | DOI | MR | Zbl

[6] Kato Y.: Rates of convergence in central limit theorem for martingale differences. Bull. Math. Statist 18 (1979), 1–8 | MR

[7] Michel R., Pfanzagl J.: The accuracy of the normal approximation for minimum contrast estimate. Z. Wahrsch. Verw. Gebiete 18 (1971), 73–84 | DOI | MR

[8] Nicholls D. F., Quinn B. G.: Random Coefficient Autoregressive Models: An Introduction. (Lecture Notes in Statistics 11.) Springer, New York 1982 | DOI | MR | Zbl

[9] Phillips P. C. B., Solo V.: Asymptotics for linear processes. Ann. Statist. 20 (1992), 971–1001 | DOI | MR | Zbl

[10] Schick A.: $\sqrt{n}$-consistent estimation in a random coefficient autoregressive model. Austral. J. Statist. 38 (1996), 155–160 | DOI | MR

[12] Vaněček P.: Estimators of generalized RCA models. In: Proc. WDS’04 Part I (2004), pp. 35–40