arXiv subjects

Abdelkader Tatachak

Publications and source records attributed to Abdelkader Tatachak.

2 recordsLinked to original sources

arXiv2025

On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications

In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as $O(n^{-1/9})$. As an application, the convergence rate in CLT of the wavelet estimator for the nonparametric regression model with LENQD errors is presented as $O(n^{-1/9})$. The performance of the main results is illustrated through a simulation study based on a real dataset.

math.ST↗

arXiv2025

On kernel mode estimation under RLT and WOD model

Let $(X_N)_{N\geq 1}$ denote a sequence of real random variables and let $\vartheta$ be the mode of the random variable of interest $X$. In this paper, we study the kernel mode estimator (say) $\vartheta_n$ when the data are widely orthant dependent (WOD) and subject to Random Left Truncation (RLT) mechanism. We establish the uniform consistency rate of the density estimator (say) $f_n$ of the underlying density $f$ as well as the almost sure convergence rate of $\vartheta_n$. The performance of the estimators are illustrated via some simulation studies and applied on a real dataset of car brake pads.

math.ST↗