Modal Regression Estimation by Local Linear Approach in High-Dimensional Data Case

This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an L1-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. As an asymptotic result, we derive the theoretical properties of the estimator by analyzing its convergence rate under the almost complete consistency framework. The result is stated under standard conditions, characterizing both the functional structure of the data and the local linear approximation properties of the model. Moreover, the expression of the convergence rate retains the usual form of the stochastic convergence rate in functional statistics. Simulations and real-data applications demonstrate the algorithm’s effectiveness, showing its advantage over existing methods in high-dimensional prediction tasks.