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

We develop goodness-of-fit (GOF) procedures rooted in Tsallis entropy, with a particular emphasis on multivariate exponential-power (generalized Gaussian) and <i>q</i>-Gaussian models. The GOF statistic compares a closed-form Tsallis entropy under the null with a non-parametric <i>k</i>-nearest-neighbor (<i>k</i>-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, <i>k</i>, and <i>q</i>. An applied example illustrates practical calibration and sensitivity, which are essential for accurate measurement.