An interpolation problem for multivariate stationary sequences

Lutz Klotz

Kybernetika (2000)

  • Volume: 36, Issue: 3, page [321]-327
  • ISSN: 0023-5954

Abstract

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Let 𝐗 and 𝐘 be stationarily cross-correlated multivariate stationary sequences. Assume that all values of 𝐘 and all but one values of 𝐗 are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

How to cite

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Klotz, Lutz. "An interpolation problem for multivariate stationary sequences." Kybernetika 36.3 (2000): [321]-327. <http://eudml.org/doc/33486>.

@article{Klotz2000,
abstract = {Let $X$ and $Y$ be stationarily cross-correlated multivariate stationary sequences. Assume that all values of $Y$ and all but one values of $X$ are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].},
author = {Klotz, Lutz},
journal = {Kybernetika},
keywords = {linear interpolation},
language = {eng},
number = {3},
pages = {[321]-327},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An interpolation problem for multivariate stationary sequences},
url = {http://eudml.org/doc/33486},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Klotz, Lutz
TI - An interpolation problem for multivariate stationary sequences
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 3
SP - [321]
EP - 327
AB - Let $X$ and $Y$ be stationarily cross-correlated multivariate stationary sequences. Assume that all values of $Y$ and all but one values of $X$ are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].
LA - eng
KW - linear interpolation
UR - http://eudml.org/doc/33486
ER -

References

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  1. Budinský P., Improvement of interpolation under additional information, In: Proceedings of the 4th Prague Symposium on Asymptotic Statistics (P. Mandl and M. Hušková, eds.), Charles University, Prague 1989, pp. 159–167 (1989) Zbl0711.62083MR1051435
  2. Makagon A., Interpolation error operator for Hilbert space valued stationary stochastic processes, Probab. Math. Statist. 4 (1984), 57–65 (1984) Zbl0575.60040MR0764330
  3. Makagon A., Weron A., q -variate minimal stationary processes, Studia Math. 59 (1976), 41–52 (1976) Zbl0412.60013MR0428419
  4. Pringle R. M., Rayner A. A., Generalized Inverse Matrices with Applications to Statistics, Griffin, London 1971 Zbl0231.15008MR0314860
  5. Rozanov, Yu. A., Stationary Random Processes (in Russian), Fizmatgiz, Moscow 1963 
  6. Salehi H., 10.1007/BF02591023, Ark. Mat. 7 (1967), 299–303 (1967) MR0233951DOI10.1007/BF02591023
  7. Salehi H., 10.1007/BF02591024, Ark. Mat. 7 (1967), 305–311 (1967) MR0236991DOI10.1007/BF02591024
  8. Weron A., On characterizations of interpolable and minimal stationary processes, Studia Math. 49 (1974), 165–183 (1974) Zbl0303.60034MR0341587

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