Non-Parametric Goodness-of-Fit Tests Using Tsallis Entropy Measures

Creative Commons License

Çadırcı M. S.

ENTROPY, cilt.27, sa.12, ss.1-20, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 12
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/e27121210
  • Dergi Adı: ENTROPY
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), INSPEC, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1-20
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

We develop goodness-of-fit (GOF) procedures rooted in Tsallis entropy, with a particular emphasis on multivariate exponential-power (generalized Gaussian) and q-Gaussian models. The GOF statistic compares a closed-form Tsallis entropy under the null with a non-parametric k-nearest-neighbor (k-NN) estimator. We establish consistency and meansquare convergence of the estimator under mild regularity and tail assumptions, discuss an asymptotic normality regime as q→ 1, and calibrate critical values by parametric bootstrap/permutation. Extensive Monte Carlo experiments report empirical size, power, and runtime. These are reported across dimensions, k, and q. An applied example illustrates practical calibration and sensitivity, which are essential for accurate measurement.