arXiv subjects

Elsayed Elamir

Publications and source records attributed to Elsayed Elamir.

6 recordsLinked to original sources

arXiv2026

Median Radial Function: A Robust, Covariance-Free Framework and Applications

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function that is robust to outliers and independent of covariance structure. The depth function does not depend on moment assumptions and naturally adapts to skewness, multimodality, and heavy-tailed distributions, which make it effective for high-dimensional data structures. We demonstrate fundamental characteristics of the underlying functionals such as subgradient and convexity. The subgradients provide additional insight and encode the imbalance in directional contributions of the data. This suggests a new approach to detect skewness and structural asymmetry through a purely radial construction. Empirical studies demonstrate that the method agrees with classical approaches under symmetry while providing a more flexible and informative characterization in complex settings.

stat.ME↗

arXiv2026

Exploring Multivariate Data Using Median Absolute Deviation Depth

We propose and analyze the moving median absolute deviation (MMAD) as a robust depth construction based on the median absolute distance functional with particular emphasis on its local geometry and probabilistic structure. In the univariate setting, we derive the derivative of the MMAD scale and interpret it through boundary mass imbalance, thereby establishing a direct connection to a robust skewness measure. This idea extends naturally to a multivariate setting that describes how observations are arranged along the 50% central region using a directional derivative, a gradient representation, and a spherical boundary distribution. From a computational perspective, MMAD can be estimated efficiently using distance calculations without needing complex optimization or projection schemes. Multivariate applications based on depth correlations, contour visualizations, and central region overlap demonstrate that MMAD identifies essentially the same central observations as classical depth notions while delivering additional information and geometric insight about directional structure. These features make MMAD a practical and informative approach for robust multivariate data analysis.

stat.ME↗

arXiv2026

Depth-Based Vector Median Absolute Deviation Moments for Robust Multivariate Shape Analysis

Classical multivariate shape analysis relies on covariance-standardized moments, such as Mardia skewness and kurtosis, which are sensitive to outliers and require finite moments. This paper introduces vector median absolute deviation (VMedAD) moments for robust multivariate shape analysis. The proposed framework replaces moment aggregation and covariance standardization with median-based center-outward contrasts defined through data depth, yielding affine equivariance and moment-free vector moments. VMedAD moments provide direction-preserving measures of multivariate skewness and directional peripheral dominance, separating central structure from tail-driven behavior. Consistency, breakdown properties, and affine equivariance are established, and simulation and real dataset examples demonstrate improved robustness and geometric interpretability over classical and projection-based methods.

stat.ME↗

arXiv2026

A Robust Moment System Based on Absolute Deviations and Quantile Slicing

This study develops two robust, quantile-sliced moment systems, mean and median absolute deviation (MAD and MedAD moments), to serve as foundational tools in parametric modeling, statistical inference, and describing distributional location, scale, skewness, and tail behavior in settings where classical moments and L-moments fail. MAD moments use block-wise absolute deviations around the median and exist whenever the mean is finite, while MedAD moments replace expectations with medians, ensuring existence for all distributions, including heavy-tailed cases with undefined mean or variance. The systems exhibit strong consistency, slice-based robustness, and bounded influence. The results indicate that MAD and L moment ratios are efficient for light to moderate tails, whereas MedAD ratios remain uniquely stable when higher moments do not exist. Applications to Cauchy parameter estimation highlight the practical value of MedAD estimators as simple, fully robust alternatives to likelihood-based approaches. Together, these systems offer a unified, median-anchored framework for reliable distributional inference under heavy tails and contamination.

stat.ME↗

arXiv2026

A Percentile-Focused Regression Method for Applied Data with Irregular Error Structures

Irregular errors such as heteroscedasticity and nonnormality remain major challenges in linear modeling. These issues often lead to biased inference and unreliable measures of uncertainty. Classical remedies, such as robust standard errors and weighted least squares, only partially address the problem and may fail when heteroscedasticity interacts with skewness or nonlinear mean structures. To address this, we propose a two-stage cumulative distribution function-based (CDF-based) beta regression framework that models the full conditional distribution of the response. The approach first transforms the outcome using a smoothed empirical CDF and then fits a flexible beta regression, allowing heteroscedasticity and nonnormality to be handled naturally through the mean-precision structure of the beta distribution. Predictions are mapped back to the original scale via the empirical quantile function, which preserves interpretability. A comprehensive Monte Carlo study shows that the proposed method consistently achieves good distributional accuracy and well-calibrated prediction intervals compared with OLS, WLS, and GLS. Application to the concrete compressive strength dataset demonstrates its stability and practical advantages.

stat.ME↗

arXiv2022

On Uses of Van der Waerden Test: A Graphical Approach

Although several nonparametric tests are available for testing population identical distributions or equal means in multiple groups problem, the Van der Waerden test has asymptotically the same efficiency as the classical one-way analysis of variance test under normality assumption where it depends on inverse normal score. In this study the Waerden test statistic is used to create a form that assists in deriving adjusted p values chart in terms of Bonferroni and Benjamini-Hochberg methods. The sampling distribution of the proposed form is derived as a gamma distribution that utilized to acquire initial p values. The proposed method will provide well recognition and deep knowledge where the changes occur. Simulation study is executed to study the characteristic of the proposed method in terms of size and power of the test and compared with original Waerden test and one-way analysis of variance test. The results are of great practical values since the proposed method stretches visible shape to decision maker to gives complete picture and deep insight where the differences happen, keep size and power of the test almost similar to original Waerden test and gives a glimpse of various information that completes the pairwise comparisons. To show the benefits of the proposed method, two applications are presented.

stat.ME↗