Article
Keywords:
linear interpolation
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].
References:
[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
MR 1051435 |
Zbl 0711.62083
[2] Makagon A.:
Interpolation error operator for Hilbert space valued stationary stochastic processes. Probab. Math. Statist. 4 (1984), 57–65
MR 0764330 |
Zbl 0575.60040
[3] Makagon A., Weron A.:
$q$-variate minimal stationary processes. Studia Math. 59 (1976), 41–52
MR 0428419 |
Zbl 0412.60013
[4] Pringle R. M., Rayner A. A.:
Generalized Inverse Matrices with Applications to Statistics. Griffin, London 1971
MR 0314860 |
Zbl 0231.15008
[5] Rozanov, Yu. A.: Stationary Random Processes (in Russian). Fizmatgiz, Moscow 1963
[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
DOI 10.1007/BF02591023 |
MR 0233951
[7] Salehi H.:
Application of the Hellinger integrals to $q$-variate stationary stochastic processes. Ark. Mat. 7 (1967), 305–311
DOI 10.1007/BF02591024 |
MR 0236991
[8] Weron A.:
On characterizations of interpolable and minimal stationary processes. Studia Math. 49 (1974), 165–183
MR 0341587 |
Zbl 0303.60034