A-optimal designs for state estimation in networks

We consider two models for estimating the expected states of nodes in networks where the observations at nodes are given by random states and measurement errors. In the first model, we assume independent successive observations at the nodes and the design question is how often the nodes should be ob...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2023-08, Vol.64 (4), p.1159-1186
Main Authors: Müller, Christine H., Schorning, Kirsten
Format: Article
Language:English
Subjects:
Configurations
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Influence
Insurance
Management
Mathematics and Statistics
Nodes
Operations Research/Decision Theory
Partial differential equations
Probability Theory and Stochastic Processes
Questions
Regular Article
Sensors
State estimation
Statistics
Statistics for Business
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Summary:We consider two models for estimating the expected states of nodes in networks where the observations at nodes are given by random states and measurement errors. In the first model, we assume independent successive observations at the nodes and the design question is how often the nodes should be observed to obtain a precise estimation of the expected states. In the second model, all nodes are observed simultaneously and the design question is to determine the nodes which need larger precision of the measurements than other nodes. Both models lead to the same design problem. We derive explicitly A -optimal designs for the most simple network with star configuration. Moreover, we consider the network with wheel configuration and derive some conditions which simplify the numerical calculation of the corresponding A -optimal designs.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-023-01435-y