On the Optimality of Sufficient Statistics-based Quantizers

DÜLEK B.

IEEE Transactions on Pattern Analysis and Machine Intelligence, cilt.45, sa.3, ss.3567-3573, 2023 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1109/tpami.2022.3172282
  • Dergi Adı: IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 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
  • Sayfa Sayıları: ss.3567-3573
  • Anahtar Kelimeler: Quantization (signal), Estimation, Random variables, Parameter estimation, Distortion, Testing, Probability distribution, Quantization, parameter estimation, Fisher information, convex analysis, hypothesis testing
  • 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.