On kernel mode estimation under RLT and WOD model

Let $(X_N{)}_{N\ge 1}$ 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.