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Related Concept Videos

Student t Distribution01:31

Student t Distribution

The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Asymptotic Normality and Convergence Rates for Tsallis Entropy Estimators via Stabilization Techniques.

Mehmet Sıddık Çadırcı1, Martin Singull2

  • 1Department of Statistics, Faculty of Science, Cumhuriyet University, 58140 Sivas, Türkiye.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary

This study introduces new methods for estimating Tsallis entropy using k-nearest neighbor techniques for Poisson and binomial data. The findings provide improved normal approximation bounds for complex statistical inference.

Keywords:
Poisson point processTsallis entropybinomial point processconvergence ratenearest-neighbor estimatornormal approximationstabilization

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Area of Science:

  • Statistical Inference
  • Information Theory
  • Spatial Statistics

Background:

  • Nearest-neighbor methods are crucial for estimating entropy in complex data.
  • Tsallis entropy offers a generalized framework for entropy estimation.
  • Existing methods face challenges with Poisson and binomial point processes.

Purpose of the Study:

  • To develop and analyze nearest-neighbor-based Tsallis entropy estimators.
  • To establish normal approximation bounds for these estimators.
  • To extend results for Shannon and Rényi entropy estimators.

Main Methods:

  • Utilizing stabilization methods combined with k-nearest neighbor validation.
  • Deriving stabilization-based normal approximation bounds for Tsallis-type k-NN functionals.
  • Employing flexible localizations of add-one costs for analysis.

Main Results:

  • Established asymptotic normality and derived convergence rates for Kolmogorov distance.
  • Recovered classical normal approximation rates (n-1/2) under stabilization.
  • Extended existing results for Shannon and Rényi entropy estimation.

Conclusions:

  • The proposed framework offers robust non-parametric statistical inference.
  • Stabilization-based normal approximations are beneficial in high-dimensional and complex spatial settings.
  • The methods enhance the estimation of Tsallis entropy for point processes.