arXiv subjects

Mehmet Sıddık Çadırcı

Publications and source records attributed to Mehmet Sıddık Çadırcı.

6 recordsLinked to original sources

arXiv2026

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

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.

math.ST↗

arXiv2026

A Nonparametric Goodness-of-Fit Test for High-Dimensional Generalized Gaussian Distributions via Nearest-Neighbor Graphs

The multivariate generalised Gaussian distribution (MGGD) is commonly used to model high-dimensional vectors with non-Gaussian radial behaviour, ranging from sharp-peaked to heavy-tailed profiles. However, because many classical multivariate tests are based on covariance inversion or high-dimensional density estimation, formal goodness-of-fit assessment for MGGD models remains challenging in modern regimes where the dimension is comparable to or exceeds the sample size. We introduce an affine-invariant, fully non-parametric goodness-of-fit procedure based on the nearest neighbour (NN) graph topology and the adapted zero principle. Following robust standardisation, we construct an independent reference sample from the adapted standardised MGGD and measure, on the combined NN graph, the cross-edge count to assess how well the observed and reference point clouds exhibit the mixture behaviour anticipated by the model. Calibration performed using a refitted parametric bootstrap accounts for nuisance-parameter uncertainty, thus ensuring reliable size under a composite specification. In this paper, we establish asymptotic validity under high-dimensional scaling and demonstrate consistency with respect to fixed elliptical departures, providing a geometric interpretation based on radial concentration and shell separation. Our simulation studies across a broad spectrum of dimensions and tail shapes reveal accurate Type I error control and robust power relative to heavy- and light-tailed alternatives, thus improving upon energy-distance benchmarks and normality-oriented graphical tests in contexts where MGGD modelling is most applicable.

stat.ME↗

arXiv2026

A Fractional M/M/1 Queue Governed by Stretched Non-Local Time Operators

We introduce a non-Markovian generalization of the classical M/M/1 queue by incorporating extended nonlocal time dynamics into Kolmogorov forward equations. We obtain the model by replacing the standard time derivative with an extended Caputo-type operator. It preserves the birth-death transition structure of the standard queue while introducing memory effects into the temporal evolution. We derive explicit representations for transient state probabilities in terms of the Kilbas-Saigo function, which naturally emerges as the relaxation kernel associated with the stretched operator, using Laplace transform techniques. We construct a time-varying interpretation and show that the fractional queue can be viewed as a distribution of a classical M/M/1 process evaluated at a non-decreasing random time. It is observed that the fractional queue can be viewed as a distribution of a classical M/M/1 process evaluated at a non-decreasing random time. We prove that under the standard stability condition $ρ<1$, the steady-state distribution remains geometric and coincides with the distribution of the classical queue, whilst we prove that the stretched fractional parameters significantly affect the convergence rate in the transient regime. Numerical examples based on Monte Carlo simulations highlight the effect of the parameters $(α,γ)$ on the distribution of empty states, tail length distributions, and the average tail evolution, and validate the flexibility of the proposed framework in capturing long-memory tail dynamics.

stat.ME↗

arXiv2025

Entropy-Based Methods to Address Sampling Bias in Archaeological Predictive Modeling

Predictive modeling in archaeology is essential for the understanding of people's behavior in the past and for guiding heritage conservation. However, spatial sampling bias caused by uneven research effort can severely limit model reliability. This research describes a novel new framework that integrates entropy-based corrections to measure and minimize such biases in archaeological modeling of foresight. Leveraging the open access data of the Grand Staircase-Escalante National Monument, we employ Shannon entropy to determine survey coverage and assign appropriate weights to pseudo-absence points. We combine these weights with predictive models such as Bayesian Spatial Logistic Regression (via R-INLA), Generalized Additive Models, Maximum Entropy and Random Forests. Our findings prove that entropy-aware models exhibit improved accuracy and robustness, especially for under-surveyed regions. This approach not only advances methodological transparency, but also improves the interpretation of archaeological prediction under conditions of data uncertainty. The proposed framework offers a scalable, theoretically grounded strategy for addressing spatial bias in archaeological datasets.

stat.AP↗

arXiv2025

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

In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop entropy-based goodness-of-fit tests based on maximum entropy formulations and nearest neighbour entropy estimators. Furthermore, we propose a novel iterative approach for estimating the shape parameters of the distributions, which is crucial for practical inference. This method extends entropy estimation techniques beyond traditional approaches, improving precision in heavy-tailed and non-Gaussian contexts. The numerical experiments are demonstrative of the statistical properties and convergence behaviour of the proposed tests. These findings are important for disciplines that require robust distributional tests, such as machine learning, signal processing, and information theory.

stat.ME↗

arXiv2024

Machine Learning Models for Accurately Predicting Properties of CsPbCl3 Perovskite Quantum Dots

Perovskite Quantum Dots (PQDs) have a promising future for several applications due to their unique properties. This study investigates the effectiveness of Machine Learning (ML) in predicting the size, absorbance (1S abs) and photoluminescence (PL) properties of $\mathrm{CsPbCl}_3$ PQDs using synthesizing features as the input dataset. the study employed ML models of Support Vector Regression (SVR), Nearest Neighbour Distance (NND), Random Forest (RF), Gradient Boosting Machine (GBM), Decision Tree (DT) and Deep Learning (DL). Although all models performed highly accurate results, SVR and NND demonstrated the best accurate property prediction by achieving excellent performance on the test and training datasets, with high $\mathrm{R}^2$ and low Root Mean Squared Error (RMSE) and low Mean Absolute Error (MAE) metric values. Given that ML is becoming more superior, its ability to understand the QDs field could prove invaluable to shape the future of nanomaterials designing.

cond-mat.mtrl-sci↗