Estimating the Conditional Density in Scalar-On-Function Regression Structure: <i>k</i>-N-N Local Linear Approach

Abstract

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator.

Keywords

• functional mixing data
• complete convergence (a.co.)
• local linear method
• distribution function
• kernel weighting
• conditional predictive region