Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques

[2608.14553] Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2608.14553 (math) [Submitted on 10 May 2026] Title: Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques Authors: Mehmet Sıddık Çadırcı , Martin Singull View a PDF of the paper titled Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques, by Mehmet S{\i}dd{\i}k \c{C}ad{\i}rc{\i} and 1 other authors View PDF HTML (experimental) Abstract: We study nearest-neighbor-based estimators of Tsallis entropy associated with Poisson and binomial point processes on general metric measure spaces. Using stabilization techniques based on flexible add-one cost operators together with second-order Poincaré inequalities, we establish asymptotic normality and derive explicit convergence rates for the Kolmogorov distance. Our analysis avoids explicit score-function decompositions and instead relies on flexible localizations of add-one costs, which simplify the treatment of higher-order terms. Under natural stabilization and moment conditions, the resulting bounds recover the classical normal approximation rates \(s^{-1/2}\) and \(n^{-1/2}\) and extend corresponding results for Shannon and Rényi entropy estimators. We further illustrate the scope of the framework through examples involving Tsallis entropy functionals, weighted \(k\)-nearest-neighbor Shannon entropy estimators. The examples provided highlight the benefits of stabilization-based normal approximations for non-parametric statistical inference in complex spatial and high-dimensional settings. Comments: 17 pages, 2 figures Subjects: Statistics Theory (math.ST) Cite as: arXiv:2608.14553 [math.ST] (or arXiv:2608.14553v1 [math.ST] for this version) https://doi.org/10.48550/arXiv.2608.14553 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mehmet Siddik Cadirci [ view email ] [v1] Sun, 10 May 2026 07:14:41 UTC (389 KB) Full-text links: Access Paper: View a PDF of the paper titled Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques, by Mehmet S{\i}dd{\i}k \c{C}ad{\i}rc{\i} and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2026-08 Change to browse by: math stat stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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