Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

Golichenko, Iryna; Moklyachuk, Mikhail

doi:10.19139/soic-2310-5070-458

Cited by 3 publications

(1 citation statement)

References 58 publications

(19 reference statements)

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“…We will suppose that the operator B has the inverse matrix. The mean-square error of the optimal estimate A ⃗ ζ is calculated by the formula (9) and is of the form…”

Section: Bulletin Of Taras Shevchenkomentioning

confidence: 99%

Extrapolation problem for periodically correlated stochastic sequences with missing observations

Golichenko

Masyutka

Moklyachuk

2021

BKNUPhM

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The problem of optimal estimation of the linear functionals $A{\zeta}=\sum_{j=1}^{\infty}{a}(j){\zeta}(j),$ 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 $j\in\{...,-n,...,-2,-1,0\}\setminus S$, $S=\bigcup _{l=1}^{s-1}\{-M_l\cdot T+1,\dots,-M_{l-1}\cdot T-N_{l}\cdot T\}$, 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 minimax-robust 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.

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“…We will suppose that the operator B has the inverse matrix. The mean-square error of the optimal estimate A ⃗ ζ is calculated by the formula (9) and is of the form…”

Section: Bulletin Of Taras Shevchenkomentioning

confidence: 99%

Extrapolation problem for periodically correlated stochastic sequences with missing observations

Golichenko

Masyutka

Moklyachuk

2021

BKNUPhM

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Filtering problem for periodically correlated stochastic sequences with missing observations

Golichenko,

Moklyachuk

2023

BKNUPhM

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The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence with missings is considered. Formulas for calculation the mean-square error and the spectral characteristic of the optimal estimate of the functionals are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, when spectral densities of sequences are not exactly known but the class of admissible spectral densities is given.

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Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

Golichenko¹,

Moklyachuk²

2020

Stat., optim. inf. comput.

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The problem of mean square optimal estimation of linear functionals which depend on the unknown values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise. Formulas for calculation the mean square errors and the spectral characteristics of the optimal estimates of functionals are derived in the case of spectral certainty, where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, where spectral densities of the sequences are not exactly known while some classes of admissible spectral densities are specified.

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Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

Cited by 3 publications

References 58 publications

Extrapolation problem for periodically correlated stochastic sequences with missing observations

Extrapolation problem for periodically correlated stochastic sequences with missing observations

Filtering problem for periodically correlated stochastic sequences with missing observations

Interpolation Problem for Periodically Correlated Stochastic Sequences with Missing Observations

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