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Invariance principle for estimates of regression coefficients of a random field. (English. Russian original) Zbl 0521.60035

Ukr. Math. J. 33, 580-586 (1982); translation from Ukr. Mat. Zh. 33, 771-778 (1981).

MSC:

60F17 Functional limit theorems; invariance principles
60G60 Random fields
60F05 Central limit and other weak theorems
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References:

[1] N. N. Leonenko and M. I. Yadrenko, ?On the asymptotic normality of least-squares estimates of regression coefficients in homogeneous and isotropic random fields,? Kibernetika, No. 2, 108-112 (1977).
[2] N. N. Leonenko, ?On estimating linear regression coefficients of homogeneous random fields,? Ukr. Mat. Zh.,30, No. 6, 749-756 (1978). · Zbl 0401.62069
[3] N. N. Leonenko and M. I. Yadrenko, ?On the invariance principle for homogeneous and isotropic random fields,? Theory Probab. Its Appl.,24, No. 1, 175-181 (1979). · Zbl 0432.60066 · doi:10.1137/1124018
[4] N. N. Leonenko and M. I. Yadrenko, ?On the invariance principle for certain classes of random fields,? Ukr. Mat. Zh.,31, 559-566 (1979).
[5] P. S. Knopov, ?On the question of estimating regression coefficients of random fields,? Kibernetika, No. 3, 112-115 (1965).
[6] Yu. A. Davydov, ?An invariance principle for stationary processes,? Theory Probab. Its Appl.,15, No. 3, 487-498 (1970). · Zbl 0219.60030 · doi:10.1137/1115050
[7] Yu. A. Davydov, ?On the convergence of distributions generated by stationary random processes,? Theory Probab. Its Appl.,13, No. 4, 691-696 (1968). · Zbl 0181.44101 · doi:10.1137/1113086
[8] A. S. Kholevo, ?The asymptotic normality of estimates of regression coefficients,? Theory Probab. Its Appl.,16, No. 4, 707-711 (1971). · Zbl 0254.62017 · doi:10.1137/1116080
[9] K. Yoshichara, ?Moment inequalities for mixing sequences,? Kodai Math. J.,18, No. 4, 316-328 (1979).
[10] A. V. Bulinskii and I. G. Zhurbenko, ?A central limit theorem for additive random functions,? Theory Probab. Its Appl.,21, No. 4, 687-697 (1976). · Zbl 0382.60025 · doi:10.1137/1121083
[11] I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen (The Netherlands) (1971).
[12] I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, Vol. 1, Springer-Verlag, Berlin (1981). · Zbl 0132.37902
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