Minimax extrapolation problem for periodically correlated stochastic sequences with missing observations
Abstract
The problem of optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence ${\zeta}(j)$ from observations of the sequence ${\zeta}(j)+{\theta}(j)$ at points $j\in\{\dots,n,\dots,2,1,0\}\setminus S$, $S=\bigcup _{l=1}^{s1}\{M_l\cdot T+1,\dots,M_{l1}\cdot TN_{l}\cdot T\}$, is considered, where ${\theta}(j)$ is an uncorrelated with ${\zeta}(j)$ periodically correlated stochastic sequence. Formulas for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional $A\zeta$ are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimaxrobust spectral characteristics of the optimal estimates of functionals are proposed in the case of spectral uncertainty, where the spectral densities are not exactly known while some sets of admissible spectral densities are specified.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06675
 Bibcode:
 2021arXiv211006675G
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability;
 60G10;
 60G25;
 60G35;
 62M20;
 93E10;
 93E11
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:2002.04383