Atıf İçin Kopyala
DÜLEK B.
IEEE Transactions on Pattern Analysis and Machine Intelligence, cilt.45, sa.3, ss.3567-3573, 2023 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
45
Sayı:
3
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Basım Tarihi:
2023
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Doi Numarası:
10.1109/tpami.2022.3172282
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Dergi Adı:
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, EMBASE, INSPEC, MEDLINE, Metadex, zbMATH, Civil Engineering Abstracts
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Sayfa Sayıları:
ss.3567-3573
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Anahtar Kelimeler:
Quantization (signal), Estimation, Random variables, Parameter estimation, Distortion, Testing, Probability distribution, Quantization, parameter estimation, Fisher information, convex analysis, hypothesis testing
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Hacettepe Üniversitesi Adresli:
Evet
Özet
IEEELet X be a random variable taking values in a set $\calX$, and let $\{P_{\theta}; \theta\in \Theta\}$ be a family of distributions indexed by the parameter vector $\theta$ taking values in a set $\Theta$. A quantized random variable $\gamma(X)$ is obtained by employing a quantizer $\gamma : \calX \rightarrow \{1,\ldots,K\}$. It is shown that any extreme point of the set of all possible probability distributions of $\gamma(X)$ can be achieved by a deterministic quantizer that decides based only on the sufficient statistics. Using this fact, optimality properties of deterministic sufficient statistics-based quantizers are established for the problem of parameter estimation. It is proven that there always exists an optimal partitioning of sufficient statistics into K convex polytopes which maximizes the trace of the Fisher information matrix when $\{P_{\theta}; \theta\in \Theta\}$ belongs to the exponential family. Furthermore, the optimality of likelihood ratio statistic for simple hypothesis testing follows as a consequence of this result, thereby demonstrating a link between parameter estimation and hypothesis testing.