<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.</p></abstract>

The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

International Laboratory of Statistics of Stochastic Processes and Quantitative Finance

Department of Higher Mathematics and System Analysis, Faculty of Engineering and Economics

Department of Electronics and Nanoelectronics, Faculty of Electrical Engineering

Department of Structural Mechanics and Applied Mathematics, Faculty of Civil Engineering

Department of Organizational and Managerial Innovations, Faculty of Management

Plekhanov Russian University of Economics

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random...

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Published Online: Nov 21, 2019

Page range: 250 - 256

Received: Jul 12, 2019

Accepted: Nov 07, 2019

DOI: https://doi.org/10.2478/msr-2019-0032

Keywords
Abrupt change of random process, unknown bandwidth, maximum likelihood method, discontinuous parameter, local Markov approximation method, bias of estimate, variance of estimate, statistical simulation

© 2019 Oleg Chernoyarov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Published Online: Nov 21, 2019

Page range: 250 - 256

Received: Jul 12, 2019

Accepted: Nov 07, 2019

DOI: https://doi.org/10.2478/msr-2019-0032

KeywordsAbrupt change of random process, unknown bandwidth, maximum likelihood method, discontinuous parameter, local Markov approximation method, bias of estimate, variance of estimate, statistical simulation

© 2019 Oleg Chernoyarov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Abrupt change of random process, unknown bandwidth, maximum likelihood method, discontinuous parameter, local Markov approximation method, bias of estimate, variance of estimate, statistical simulation