On the Kernel Conditional Density Estimator with Functional Explanatory Variable

This article focuses on the relationship between a scalar-explained random variable Y and a functional explanatory random variable X. Indeed, Through this work, we aim to estimate the conditional probability density f (y/x) when the explanatory variable X is functional using the kernel method. More precisely, we will present a numerical application based on simulated samples, with the aim of, on the one hand, highlighting the implementation of the estimator in question and the impact of using a symmetric kernel on its quality. On the other hand, analyzing the performance of this estimator as a function of the sample size, the hypothesis imposed on the smoothing parameters (The smoothing parameters in the X direction and the Y direction are independent and the smoothing parameter in the X direction is the same as that in the Y direction) and the norm used in its construction. AMS subject classification. Primary 62G05; 62G07; Secondary 62R10. Communicated Editor: A. Necir. 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