Geodesic
Minimax prediction problem for multidimensional stationary stochastic sequences
Teoriâ slučajnyh processov, Tome 14 (2008) no. 4, pp. 89-109.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{THSP_2008_14_4_a0,
     author = {Mikhail Moklyachuk and Aleksandr Masyutka},
     title = {Minimax prediction problem for multidimensional stationary stochastic sequences},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {89--109},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a0/}
}
TY  - JOUR
AU  - Mikhail Moklyachuk
AU  - Aleksandr Masyutka
TI  - Minimax prediction problem for multidimensional stationary stochastic sequences
JO  - Teoriâ slučajnyh processov
PY  - 2008
SP  - 89
EP  - 109
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a0/
LA  - en
ID  - THSP_2008_14_4_a0
ER  - 
%0 Journal Article
%A Mikhail Moklyachuk
%A Aleksandr Masyutka
%T Minimax prediction problem for multidimensional stationary stochastic sequences
%J Teoriâ slučajnyh processov
%D 2008
%P 89-109
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a0/
%G en
%F THSP_2008_14_4_a0
Mikhail Moklyachuk; Aleksandr Masyutka. Minimax prediction problem for multidimensional stationary stochastic sequences. Teoriâ slučajnyh processov, Tome 14 (2008) no. 4, pp. 89-109. http://geodesic.mathdoc.fr/item/THSP_2008_14_4_a0/

[1] Akhiezer, N. I., Glazman, I. M., Teoriya lineinykh operatorov v gilbertovom npostranstve, Nauka, M., 1906 | MR

[2] Grenander, U., Sege, G., Teplitsevi formy i ikh primeneniya, IL, M., 1961

[3] Guld, S., Variatsionnye metody v zadachakh na sobstvennye znacheniya, Nauka, M., 1970

[4] Franke, L., “On the robust prediction and interpolation of time series in the presence of correlated noise”, J. Time Series Analysis, 5:4 (1984), 227–244 | DOI | MR | Zbl

[5] Franke. J., “Minimax robust prediction of discrete time series”, Z. Wahrsch. Verw. Gebiete., 68 (1985), 337–364 | DOI | MR | Zbl

[6] Franke, J. Poor, H. V., “Minimax-robust filtering and finite-length robust predictors”, Robust and Nonlinear Time Series, Analysis.Lecture Notes in Statistics, 26, Springer-Verlag, Heidelberg, 1984, 87—126 | DOI | MR | Zbl

[7] Franke, ]., “A general version of Breimarrs minimax filter”, Note di Matcmatica., 11 (1991), 157–175 | MR | Zbl

[8] Grenander, U., “A prediction problem in game theory”, Ark. Mat., 3 (1957), 371–379 | DOI | MR | Zbl

[9] Kailath, T., “A view of three decades of linear filtering theory”, IEEE Trans. on Inform. Theory, 20:2 (1974), 146–181 | DOI | MR | Zbl

[10] Kassam, S. A., Poor. H. V., “Robust techniques for signal processing: A survey”, Proc. IEEE., 73:3 (1985), 433–481 | DOI | Zbl

[11] Kolmogorov, A. N., Selected works of A. N. Kolmogorov, v. II, Mathematics and Its Applications. Soviet Series, 26, Probability theory and mathematical statistics, ed. A. N. Shiryayev, Kluwer Academic Publishers, Dordrecht, 1992 | MR | Zbl

[12] Moklvachuk, M. P., “Stochastic autoregressive sequence and minimax interpolation”, Theor. Probab. and Math. Stat., 48 (1994), 95–103 | MR

[13] Moklvachuk Mikhail, “Estimates of stochastic processes from observations with noise”, Theory Stoch. Process., 3(19):3-4 (1997), 330–338

[14] Moklvachuk, M. P., “Extrapolation of stationary sequences from observations with noise”, Theor. Probab. and Math. Stat., 57 (1998), 133–141 | MR

[15] Moklvachuk, Mikhail, “Robust procedures in time series analysis”, Theory Stoch. Process., 6(22):3-4 (2000), 127–147

[16] Moklvachuk, Mikhail, “Game theory and convex optimization methods in robust estimation problems”, Theory Stoch. Process., 7(23):1-2 (2001), 253–264

[17] Moklvachuk, M. P., Masyutka, A. Yu., “Interpolation of vector-valued stationary sequences”, Theor. Probab. and Math. Stat., 73 (2005), 112–119 | MR

[18] Moklvachuk, M. P., Masyutka, A. Yu., “Extrapolation of vector-valued stationary sequences”, Visn.. Ser. Fiz.-Mat. Nauky. Kyiv. Univ. Im. Tarasa Shevchenka, 3 (2005), 60–70

[19] Moklvachuk, Mikhail P., Masyutka, Aleksandr Yu., “Extrapolation of multidimensional stationary processes”, Random Oper. and Stoch. Equ., 14 (2006), 233–244 | DOI | MR

[20] | MR | Zbl

[21] Vastola, K. S., Poor, H. V., “An analysis of the effects of spectra! uncertainty on Wiener filtering”, Automatica, 28 (1983), 289–293 | DOI | MR

[22] Wiener, N., Extrapolation, interpolation, and smoothing of stationary time series. With engineering applications, Mass.: The M. I. T. Press, Massachusetts Institute of Technology, Cambridge, 1966 | MR | Zbl

[23] Yaglom, A. M., Correlation theory of stationary and related random functions, v. I, Basic results, Springer-Yerlag. Springer Series in Statistics, New York etc., 1987 | MR

[24] Yaglom, A. M., Correlation theory of stationary and related, random functions, v. II, Supplementary notes and references, Springer-Yerlag. Springer Series in Statistics, New York etc., 1987 | MR