Interpolation Problems for Random Fields from Observations in Perforated Plane

Автор(и)

  • Михайло Павлович Моклячук Київський національний університет імені Тараса Шевченка, Ukraine
  • Наталія Юріївна Щестюк Національний університет «Києво-Могилянська академія», Ukraine
  • Анастасія Сергіївна Флоренко Національний університет «Києво-Могилянська академія»,

DOI:

https://doi.org/10.32626/2308-5916.2016-14.83-97

Анотація

The problem of estimation of linear functionals which depend on the unknown values of a homogeneous random field  in the region  from observations of the sum  at points  is investigated. Formulas for calculating the mean square errors and the spectral characteristics of the optimal linear estimate of functionals are derived in the case where the spectral densities are exactly known. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics are proposed in the case where the spectral densities are not exactly known while a class of admissible spectral densities is given.

Посилання

Kolmogorov A. N. Selected works of A. N. Kolmogorov / A. N. Kolmogorov // Mathematics and Its Applications. Soviet Series. 26. — Dordrecht : Kluwer Academic Publishers, 1999. — Vol. II: Probability theory and mathematical statistics. — 597 p.

Wiener N. Extrapolation, interpolation, and smoothing of stationary time series. With engineering applications / N. Wiener. — Cambridge : The M. I. T. Press, Massachusetts Institute of Technology, 1966. — 163 p.

Yaglom A. M. Correlation theory of stationary and related random functions / A. M. Yaglom // Springer Series in Statistics. — New York etc. : Springer-Verlag, 1987. — Vol. I: Basic results. — 526 p.

Yaglom A. M. Correlation theory of stationary and related random functions / A. M. Yaglom // Springer Series in Statistics. — New York etc. : Springer-Verlag, 1987. — Vol. II: Supplementary notes and references. — 258 p.

Yadrenko, M. I. Spectral theory of random fields. New York: Optimization Software / M. I. Yadrenko. — New York ; Heidelberg ; Berlin : Springer-Verlag, 1983. — 259 p.

Vastola K. S. An analysis of the effects of spectral uncertainty on Wiener filtering / K. S Vastola, H. V. Poor // Automatica. — 1983. — Vol. 28. — P. 289–293.

Kassam S. A. Robust techniques for signal processing / S. A. Kassam, H. V. Poor // Asurvey, Proc. IEEE. — 1985. — Vol 73, № 3. — P. 433–481.

Moklyachuk, M. P. Stochastic autoregressive sequence and minimax interpolation / M. P. Moklyachuk // Theor. Probab. and Math. Stat. — 1994. — Vol. 48. — P. 95–103.

Moklyachuk M. Estimates of stochastic processes from observations with noise / M. Moklyachuk // Theory Stoch. Process. — 1997. Vol 3(19), № 3–4. — P. 330–338.

Moklyachuk M. Robust procedures in time series analysis / M. Moklyachuk // Theory Stoch. Process. — 2000. — Vol. 6 (22), № 3-4. — P. 127–147.

Moklyachuk M. P. Minimax-robust extrapolation problem for continuous random fields / M. P. Moklyachuk, N. Yu. Shchestyuk // Visn., Ser. Fiz.-Mat. Nauky. Kyiv. Univ. im. Tarasa Shevchenka, 2002. — P. 47–57.

Moklyachuk M. P. On the filtering problem for random fields / M. P. Moklyachuk, N. Yu. Shchestyuk // Visn., Mat. Mekh. Kyiv. Univ. im. Tarasa Shevchenka, 2002. — P. 116–125.

Moklyachuk M. P. Extrapolation of random fields observed with noise / M. P. Moklyachuk, N. Yu Shchestyuk // Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauk. — 2003. — № 4. — P. 12–17.

Moklyachuk M. P. On robust estimates of random fields / M. P. Moklyachuk, N. Yu Shchestyuk // Visn., Ser. Fiz.-Mat. Nauky. Kyiv. Univ. Im. Tarasa Shevchenka. — 2003. — P. 32–41.

Moklyachuk M. P. Estimation problems for random fields from observations in discrete moments of time / M. P. Moklyachuk, N. Yu Shchestyuk // Theory of Stochastic Processes. — 2004. — Vol. 10 (26), № 1–2. — P. 141–154.

Moklyachuk M. P. Robust estimates of functionals of homogeneous random fields / M. P. Moklyachuk, N. Yu Shchestyuk // Theory of Stochastic Processes. — 2003. — Vol. 9 (25), № 1. — P. 101–113.

Moklyachuk M. P. On a linear prediction problem for homogeneous random fields / M. P. Moklyachuk, S. V. Tatarinov // Theor. Probab. and Math. Stat. — 1993. — Vol. 47. — P. 119–127.

Моклячук М. П. Оцінки функціоналів від випадкових полів / М. П. Моклячук, Н. Ю. Щестюк. — Ужгород : АУТДОР-ШАРК, 2013. — С. 228.

Moklyachuk M. P. Interpolation Problem for Stationary Sequences with Missing Observations / M. Moklyachuk M. Sidesh // Statistics, Optimization & Information Computing. — 2015. — Vol. 3, № 3. — Р. 259–275.

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Опубліковано

2016-09-13

Номер

2016: Математичне та комп'ютерне моделювання. Серія: Технічні науки. Випуск 14

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