The \(k\)-Nearest Neighbour Local Linear Estimation of the Conditional Hazard Function in High-Dimensional Statistics

Local linear fitting has demonstrated several convincing statistical properties, especially in multivariate analysis. However, with the increasing importance of functional data analysis in the field of data science, local polynomials have become a significant focus in this research area. This paper focuses on estimating of the conditional hazard function of a scalar response variable with a functional random variable. A novel estimator is proposed by combining the \(k\) -nearest neighbors ( \(k\) -NN) procedure with the local linear approach. The resulting estimator has many advantages from the two approaches (kNN and LLE methods). This is supported by the established asymptotic normality with explicit rates of the constructed estimator. As an application, the asymptotic con-fidence bands for the conditional hazard model based on the \(k\) -Nearest Neighbors Local Linear Estimator is presented. A simulation study, conducted to assess finite sample behavior, demonstrates the superiority of our new estimator than the classical kernel method.