Estimation of Stochastic Processes with Missing Observations

Mikhail Moklyachuk
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Maria Sidei
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Oleksandr Masyutka
Department of Mathematics and Theoretical Radiophysics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Series: Mathematics Research Developments
BISAC: MAT029040

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$230.00

Volume 10

Issue 1

Volume 2

Volume 3

Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing.

Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.
(Imprint: Nova)

Preface

Chapter 1. Estimation of Functionals from Stationary Stochastic Sequences with Missing Observations

Chapter 2. Estimation of Functionals from Stationary Stochastic Processes with Missing Observations

Chapter 3. Estimation of Functionals from Multidimensional Stationary Stochastic Sequences with Missing Observations

Chapter 4. Estimation of Multidimensional Continuous Time Stationary Stochastic Processes with Missing Observations

Index

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