A Fundamental Limitation on Maximum Parameter Dimension for Accurate Estimation with Quantized Data
It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which doesn't depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system.
J. Zhang, "A Fundamental Limitation on Maximum Parameter Dimension for Accurate Estimation with Quantized Data," IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers (IEEE), Jun 2018.
The definitive version is available at https://doi.org/10.1109/TIT.2018.2850968
Electrical and Computer Engineering
Keywords and Phrases
Distributed Sensor Parameter Estimation; Inestimable Dimension for Quantized Data; Singular Fisher Information Matrix; Identifiability; Quantization
International Standard Serial Number (ISSN)
0018-9448 ; 1557-9654
Article - Journal
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