December 4, 2025Open Access

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

MÇMehmet Sıddık ÇadırcıSivas Cumhuriyet Üniversitesi

Key Points

The goodness-of-fit tests demonstrate significant power, enhancing the accuracy of statistical measurements.
The k-nearest-neighbor estimator consistently achieves mean-square convergence under specific assumptions.
This analysis utilizes Monte Carlo experiments to evaluate the empirical size and runtime across multiple dimensions.
The findings underscore the importance of calibration for effective model fitting, particularly in high-dimensional spaces.

Abstract

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 mean-square 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.

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