Sergiy Shklyar's Books

Radiation Risk Estimation

Based on Measurement Error Models

By: Sergii Masiuk,Alexander Kukush,Sergiy Shklyar,Mykola Chepurny,Illya Likhtarov

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Radiation Risk Estimation

Based on Measurement Error Models

By: Sergii Masiuk,Alexander Kukush,Sergiy Shklyar,Mykola Chepurny,Illya Likhtarov

This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariates Measurement error models Linear models with classical error Polynomial regression with known variance of classical error Nonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure doses Overview of risk models realized in program package EPICURE Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident Elements of estimating equations theory Consistency of efficient methods Efficient SIMEX method as a combination of the SIMEX method and the corrected score method Application of regression calibration in the model with additive error in exposure doses

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Page Count

270

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110433664

ISBN 13

9783110433661

Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

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Fractional Brownian Motion

Approximations and Projections

By: Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar

This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.

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