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arXiv · 2412.07874

On kernel mode estimation under RLT and WOD model

Mohamed Kaber El Alem·Zohra Guessoum·Abdelkader Tatachak
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Abstract

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.

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Mohamed Kaber El Alem, Zohra Guessoum, Abdelkader Tatachak. 2024-12-10. On kernel mode estimation under RLT and WOD model. https://arxiv.org/abs/2412.07874

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