On kernel mode estimation under RLT and WOD model

TL;DR

This paper investigates the consistency and convergence rates of kernel mode estimators for data with Random Left Truncation and Wide Orthant Dependence, supported by simulations and real data application.

Contribution

It introduces the analysis of kernel mode estimation under RLT and WOD conditions, providing theoretical convergence rates and practical validation.

Findings

Established uniform consistency rate of density estimator

Proved almost sure convergence rate of the mode estimator

Validated results through simulations and real data analysis

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.