Mean Square Error of the Conditional Quantile Function in the Local Linear Estimation for Functional Data

A. In this paper, we investigate the asymptotic mean square error and the convergence rates of an estimator constructed using the local linear method for estimating the conditional mode function.Under fairly general regularity conditions, we derive explicit expressions for both the bias and the variance of the estimator.To highlight the practical relevance of our approach, we provide an application to real data, illustrating the effectiveness and potential advantages of this mode-based estimation method compared to the classical conditional quantile estimation.