| Title:
|
An interpolation problem for multivariate stationary sequences (English) |
| Author:
|
Klotz, Lutz |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
[321]-327 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let {\boldmath$X$} and {\boldmath$Y$} be stationarily cross-correlated multivariate stationary sequences. Assume that all values of {\boldmath$Y$} and all but one values of {\boldmath$X$} 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]. (English) |
| Keyword:
|
linear interpolation |
| MSC:
|
60G10 |
| MSC:
|
60G25 |
| MSC:
|
62H20 |
| MSC:
|
62M20 |
| MSC:
|
62M99 |
| idZBL:
|
Zbl 1243.62124 |
| idMR:
|
MR1773507 |
| . |
| Date available:
|
2009-09-24T19:33:11Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135353 |
| . |
| Reference:
|
[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 Zbl 0711.62083, MR 1051435 |
| Reference:
|
[2] Makagon A.: Interpolation error operator for Hilbert space valued stationary stochastic processes.Probab. Math. Statist. 4 (1984), 57–65 Zbl 0575.60040, MR 0764330 |
| Reference:
|
[3] Makagon A., Weron A.: $q$-variate minimal stationary processes.Studia Math. 59 (1976), 41–52 Zbl 0412.60013, MR 0428419 |
| Reference:
|
[4] Pringle R. M., Rayner A. A.: Generalized Inverse Matrices with Applications to Statistics.Griffin, London 1971 Zbl 0231.15008, MR 0314860 |
| Reference:
|
[5] Rozanov, Yu. A.: Stationary Random Processes (in Russian).Fizmatgiz, Moscow 1963 |
| Reference:
|
[6] Salehi H.: The Hellinger square–integrability of matrix–valued measures with respect to a non–negative hermitian measure.Ark. Mat. 7 (1967), 299–303 MR 0233951, 10.1007/BF02591023 |
| Reference:
|
[7] Salehi H.: Application of the Hellinger integrals to $q$-variate stationary stochastic processes.Ark. Mat. 7 (1967), 305–311 MR 0236991, 10.1007/BF02591024 |
| Reference:
|
[8] Weron A.: On characterizations of interpolable and minimal stationary processes.Studia Math. 49 (1974), 165–183 Zbl 0303.60034, MR 0341587 |
| . |
