Nonparametric conditional mode estimate under doubly truncated model

Conditional mode function is often used in various fields such as statistics, data analysis, and machine learning to understand the distribution of data and make decisions based on specific conditions or criteria. In this paper, we propose a non-parametric kernel estimator of the conditional mode function, when the variable of interest is subject to random doubly truncation. We prove the suggested estimator's strong consistency with a rate and state its asymptotic normality under some regularity assumptions. Our results are based on special mathematical techniques such as the iterative non-parametric maximum likelihood estimators (NPMLE) of the distribution function and the Vapnik-Cervonenkis classes for which uniform exponential inequalities are available. This study will be a valuable resource for scholars and practitioners interested in non-parametric kernel estimation methods for doubly truncated data.